Invariant Table Check a Knot Higher Crossing Crossref Virtual Knots Please cite FlatKnotInfo

Flat knot 4.1

Min(phi) over symmetries of the knot is: [-3,-1,2,2,1,2,3,1,2,0]
Flat knots (up to 7 crossings) with same phi are :['4.1']
Arrow polynomial of the knot is: -2K1K2 + K1 + K3 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['4.1', '4.3', '6.59', '6.66', '6.112', '6.215', '6.297', '6.306', '6.346', '6.351', '6.352', '6.353', '6.368', '6.393', '6.398', '6.402', '6.420', '6.422', '6.524', '6.529', '6.630', '6.632', '6.633', '6.642', '6.684', '6.707', '6.708', '6.717', '6.719', '6.721', '6.722', '6.737', '6.793', '6.835', '6.837', '6.847', '6.849', '6.857', '6.858', '6.883', '6.902', '6.913', '6.1084', '6.1092', '6.1097', '6.1136', '6.1146', '6.1155', '6.1159', '6.1374', '7.349', '7.365', '7.690', '7.2260', '7.2269', '7.2612', '7.2624', '7.2972', '7.2975', '7.4214', '7.4542', '7.4546', '7.9686', '7.9695', '7.9947', '7.10639', '7.10643', '7.10829', '7.10833', '7.13433', '7.15124', '7.15128', '7.15638', '7.15647', '7.15703', '7.15845', '7.16115', '7.16120', '7.16150', '7.19418', '7.19470', '7.19474', '7.19871', '7.20310', '7.20362', '7.20421', '7.20424', '7.23942', '7.24011', '7.24100', '7.24114', '7.24116', '7.24445', '7.26258', '7.26318', '7.26811', '7.26827', '7.27967', '7.28040', '7.28124', '7.28138', '7.29092', '7.29107', '7.29452', '7.29853', '7.30091', '7.30098', '7.30140', '7.30193', '7.30339', '7.30350', '7.30354']
Outer characteristic polynomial of the knot is: t^5+37t^3+11t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['4.1']
2-strand cable arrow polynomial of the knot is: -128K12K2*2 + 48K1*2K2 - 88K12 + 64K1K23K3 + 224K1K2K3 + 16K1K3K4 - 32K24 - 64K2*2K3*2 - 8K2*2K4*2 + 8K2*2K4 - 54K22 + 16K2K3K5 + 8K2K4K6 - 88K3*2 - 12K4*2 - 2K6**2 + 90
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['4.1']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk4.83', 'vk4.87', 'vk4.88', 'vk4.93', 'vk4.97', 'vk4.103', 'vk6.16365', 'vk6.16408', 'vk6.17020', 'vk6.17022', 'vk6.17027', 'vk6.17262', 'vk6.17263', 'vk6.17270', 'vk6.18108', 'vk6.18252', 'vk6.18254', 'vk6.18255', 'vk6.18257', 'vk6.18446', 'vk6.18587', 'vk6.18589', 'vk6.18592', 'vk6.18594', 'vk6.20030', 'vk6.20031', 'vk6.20038', 'vk6.20039', 'vk6.20101', 'vk6.20103', 'vk6.20108', 'vk6.20110', 'vk6.20308', 'vk6.20309', 'vk6.20310', 'vk6.20311', 'vk6.20381', 'vk6.20382', 'vk6.20383', 'vk6.20384', 'vk6.20557', 'vk6.20564', 'vk6.20565', 'vk6.20637', 'vk6.20638', 'vk6.20639', 'vk6.20640', 'vk6.21302', 'vk6.21303', 'vk6.21319', 'vk6.21320', 'vk6.21379', 'vk6.21381', 'vk6.21387', 'vk6.21388', 'vk6.21643', 'vk6.21644', 'vk6.21647', 'vk6.21648', 'vk6.21722', 'vk6.21724', 'vk6.21725', 'vk6.21727', 'vk6.21958', 'vk6.21969', 'vk6.21970', 'vk6.22066', 'vk6.22067', 'vk6.22068', 'vk6.22069', 'vk6.22697', 'vk6.22798', 'vk6.23439', 'vk6.23441', 'vk6.23452', 'vk6.23741', 'vk6.23742', 'vk6.23751', 'vk6.24557', 'vk6.24732', 'vk6.24734', 'vk6.24735', 'vk6.24737', 'vk6.24976', 'vk6.25144', 'vk6.25147', 'vk6.27080', 'vk6.27081', 'vk6.27098', 'vk6.27099', 'vk6.27174', 'vk6.27176', 'vk6.27188', 'vk6.27190', 'vk6.27603', 'vk6.27604', 'vk6.27607', 'vk6.27608', 'vk6.27701', 'vk6.27702', 'vk6.27705', 'vk6.27706', 'vk6.28013', 'vk6.28026', 'vk6.28027', 'vk6.28121', 'vk6.28122', 'vk6.28125', 'vk6.28126', 'vk6.28783', 'vk6.28784', 'vk6.28793', 'vk6.28794', 'vk6.28857', 'vk6.28859', 'vk6.28872', 'vk6.28873', 'vk6.29155', 'vk6.29156', 'vk6.29157', 'vk6.29158', 'vk6.29245', 'vk6.29247', 'vk6.29250', 'vk6.29252', 'vk6.29479', 'vk6.29486', 'vk6.29487', 'vk6.34668', 'vk6.35515', 'vk6.35517', 'vk6.35526', 'vk6.35528', 'vk6.35963', 'vk6.35964', 'vk6.35976', 'vk6.35978', 'vk6.36698', 'vk6.36859', 'vk6.36861', 'vk6.36864', 'vk6.36866', 'vk6.37322', 'vk6.37328', 'vk6.38476', 'vk6.38477', 'vk6.38482', 'vk6.38483', 'vk6.38585', 'vk6.38587', 'vk6.38600', 'vk6.38602', 'vk6.39029', 'vk6.39030', 'vk6.39031', 'vk6.39032', 'vk6.39139', 'vk6.39141', 'vk6.39146', 'vk6.39148', 'vk6.39425', 'vk6.39426', 'vk6.39431', 'vk6.39432', 'vk6.39553', 'vk6.39554', 'vk6.39555', 'vk6.39556', 'vk6.40667', 'vk6.40668', 'vk6.40679', 'vk6.40680', 'vk6.40773', 'vk6.40775', 'vk6.40788', 'vk6.40789', 'vk6.41280', 'vk6.41281', 'vk6.41284', 'vk6.41285', 'vk6.41619', 'vk6.41620', 'vk6.41627', 'vk6.41628', 'vk6.41779', 'vk6.41780', 'vk6.41781', 'vk6.41782', 'vk6.42325', 'vk6.42933', 'vk6.42935', 'vk6.42940', 'vk6.42942', 'vk6.43228', 'vk6.43229', 'vk6.43235', 'vk6.43237', 'vk6.43974', 'vk6.44085', 'vk6.44087', 'vk6.44088', 'vk6.44090', 'vk6.45361', 'vk6.45362', 'vk6.45373', 'vk6.45374', 'vk6.45469', 'vk6.45471', 'vk6.45476', 'vk6.45478', 'vk6.45875', 'vk6.45877', 'vk6.45878', 'vk6.45880', 'vk6.46004', 'vk6.46005', 'vk6.46014', 'vk6.46015', 'vk6.46163', 'vk6.46164', 'vk6.46167', 'vk6.46168', 'vk6.47126', 'vk6.47127', 'vk6.47132', 'vk6.47133', 'vk6.47205', 'vk6.47207', 'vk6.47213', 'vk6.47214', 'vk6.47678', 'vk6.47679', 'vk6.47684', 'vk6.47685', 'vk6.54659', 'vk6.56050', 'vk6.56052', 'vk6.56055', 'vk6.56057', 'vk6.56222', 'vk6.57170', 'vk6.57171', 'vk6.57172', 'vk6.57173', 'vk6.57245', 'vk6.57246', 'vk6.57249', 'vk6.57250', 'vk6.57539', 'vk6.57540', 'vk6.57541', 'vk6.57542', 'vk6.58365', 'vk6.58366', 'vk6.58369', 'vk6.58370', 'vk6.59183', 'vk6.60607', 'vk6.60612', 'vk6.60821', 'vk6.61874', 'vk6.61875', 'vk6.61882', 'vk6.61883', 'vk6.65721', 'vk6.65724', 'vk6.66784', 'vk6.66785', 'vk6.66786', 'vk6.66787', 'vk6.71313', 'vk6.71316', 'vk6.71321', 'vk6.71324', 'vk6.71329', 'vk6.71332', 'vk6.71337', 'vk6.71340', 'vk6.71673', 'vk6.71676', 'vk6.71686', 'vk6.71689', 'vk6.71694', 'vk6.71697', 'vk6.71708', 'vk6.71711', 'vk6.71742', 'vk6.71745', 'vk6.71766', 'vk6.71769', 'vk6.72088', 'vk6.72091', 'vk6.72104', 'vk6.72107', 'vk6.72112', 'vk6.72115', 'vk6.72126', 'vk6.72129', 'vk6.72162', 'vk6.72165', 'vk6.72186', 'vk6.72189', 'vk6.73468', 'vk6.73474', 'vk6.73478', 'vk6.73484', 'vk6.73541', 'vk6.73543', 'vk6.73550', 'vk6.73552', 'vk6.73753', 'vk6.73807', 'vk6.73809', 'vk6.73959', 'vk6.73961', 'vk6.74006', 'vk6.74008', 'vk6.74068', 'vk6.74069', 'vk6.74107', 'vk6.74114', 'vk6.74117', 'vk6.74121', 'vk6.74145', 'vk6.74147', 'vk6.74168', 'vk6.74169', 'vk6.74172', 'vk6.74173', 'vk6.74347', 'vk6.74348', 'vk6.74484', 'vk6.74488', 'vk6.74493', 'vk6.74496', 'vk6.74501', 'vk6.74504', 'vk6.74515', 'vk6.74518', 'vk6.74521', 'vk6.74524', 'vk6.74532', 'vk6.74534', 'vk6.74633', 'vk6.74634', 'vk6.74676', 'vk6.74684', 'vk6.74687', 'vk6.74692', 'vk6.74714', 'vk6.74716', 'vk6.74768', 'vk6.74769', 'vk6.74776', 'vk6.74777', 'vk6.74990', 'vk6.74991', 'vk6.75002', 'vk6.75226', 'vk6.75232', 'vk6.75235', 'vk6.75239', 'vk6.75294', 'vk6.75296', 'vk6.75307', 'vk6.75309', 'vk6.75477', 'vk6.75482', 'vk6.75486', 'vk6.75490', 'vk6.75696', 'vk6.75710', 'vk6.75776', 'vk6.75778', 'vk6.75931', 'vk6.75934', 'vk6.75937', 'vk6.75939', 'vk6.75942', 'vk6.75945', 'vk6.75950', 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'vk6.85199', 'vk6.85203', 'vk6.85206', 'vk6.85210', 'vk6.85282', 'vk6.85286', 'vk6.85290', 'vk6.85292', 'vk6.85326', 'vk6.85330', 'vk6.85340', 'vk6.85344', 'vk6.85390', 'vk6.85394', 'vk6.85404', 'vk6.85530', 'vk6.85532', 'vk6.85692', 'vk6.85695', 'vk6.85697', 'vk6.85807', 'vk6.85811', 'vk6.86026', 'vk6.86032', 'vk6.86034', 'vk6.86040', 'vk6.86058', 'vk6.86059', 'vk6.86063', 'vk6.86065', 'vk6.86068', 'vk6.86073', 'vk6.86077', 'vk6.86079', 'vk6.86092', 'vk6.86095', 'vk6.86101', 'vk6.86103', 'vk6.86112', 'vk6.86122', 'vk6.86126', 'vk6.86132', 'vk6.86135', 'vk6.86137', 'vk6.86143', 'vk6.86145', 'vk6.86150', 'vk6.86153', 'vk6.86158', 'vk6.86161', 'vk6.86269', 'vk6.86271', 'vk6.86289', 'vk6.86294', 'vk6.86331', 'vk6.86333', 'vk6.86337', 'vk6.86356', 'vk6.86571', 'vk6.86573', 'vk6.86588', 'vk6.86590', 'vk6.86642', 'vk6.86649', 'vk6.86651', 'vk6.86657', 'vk6.86659', 'vk6.86712', 'vk6.86714', 'vk6.86772', 'vk6.86773', 'vk6.86782', 'vk6.86783', 'vk6.86788', 'vk6.86789', 'vk6.86792', 'vk6.86793', 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'vk6.89927', 'vk6.89932', 'vk6.89935', 'vk6.89945', 'vk6.89946', 'vk6.89953', 'vk6.89988', 'vk6.89989', 'vk6.89993', 'vk6.89995', 'vk6.89998', 'vk6.90003', 'vk6.90011', 'vk6.90014', 'vk6.90015', 'vk6.90018', 'vk6.90023', 'vk6.90027', 'vk6.90028', 'vk6.90031', 'vk6.90045', 'vk6.90049']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is +.
The reverse -K is
The reversed mirror image -K* is
The fillings (up to the first 10) associated to the algebraic genus:
Or click here to check the fillings

Min(phi) over symmetries of the knot is: [-3,-1,2,2,1,2,3,1,2,0]

Flat knots (up to 7 crossings) with same phi are :['4.1']

Arrow polynomial of the knot is: -2*K1*K2 + K1 + K3 + 1

Flat knots (up to 7 crossings) with same arrow polynomial are :['4.1', '4.3', '6.59', '6.66', '6.112', '6.215', '6.297', '6.306', '6.346', '6.351', '6.352', '6.353', '6.368', '6.393', '6.398', '6.402', '6.420', '6.422', '6.524', '6.529', '6.630', '6.632', '6.633', '6.642', '6.684', '6.707', '6.708', '6.717', '6.719', '6.721', '6.722', '6.737', '6.793', '6.835', '6.837', '6.847', '6.849', '6.857', '6.858', '6.883', '6.902', '6.913', '6.1084', '6.1092', '6.1097', '6.1136', '6.1146', '6.1155', '6.1159', '6.1374', '7.349', '7.365', '7.690', '7.2260', '7.2269', '7.2612', '7.2624', '7.2972', '7.2975', '7.4214', '7.4542', '7.4546', '7.9686', '7.9695', '7.9947', '7.10639', '7.10643', '7.10829', '7.10833', '7.13433', '7.15124', '7.15128', '7.15638', '7.15647', '7.15703', '7.15845', '7.16115', '7.16120', '7.16150', '7.19418', '7.19470', '7.19474', '7.19871', '7.20310', '7.20362', '7.20421', '7.20424', '7.23942', '7.24011', '7.24100', '7.24114', '7.24116', '7.24445', '7.26258', '7.26318', '7.26811', '7.26827', '7.27967', '7.28040', '7.28124', '7.28138', '7.29092', '7.29107', '7.29452', '7.29853', '7.30091', '7.30098', '7.30140', '7.30193', '7.30339', '7.30350', '7.30354']

Outer characteristic polynomial of the knot is: t^5+37t^3+11t

Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['4.1']

2-strand cable arrow polynomial of the knot is: -128*K1**2*K2**2 + 48*K1**2*K2 - 88*K1**2 + 64*K1*K2**3*K3 + 224*K1*K2*K3 + 16*K1*K3*K4 - 32*K2**4 - 64*K2**2*K3**2 - 8*K2**2*K4**2 + 8*K2**2*K4 - 54*K2**2 + 16*K2*K3*K5 + 8*K2*K4*K6 - 88*K3**2 - 12*K4**2 - 2*K6**2 + 90

Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['4.1']

Virtual knots (up to 6 crossings) projecting to this knot are :'vk4.83', 'vk4.87', 'vk4.88', 'vk4.93', 'vk4.97', 'vk4.103', 'vk6.16365', 'vk6.16408', 'vk6.17020', 'vk6.17022', 'vk6.17027', 'vk6.17262', 'vk6.17263', 'vk6.17270', 'vk6.18108', 'vk6.18252', 'vk6.18254', 'vk6.18255', 'vk6.18257', 'vk6.18446', 'vk6.18587', 'vk6.18589', 'vk6.18592', 'vk6.18594', 'vk6.20030', 'vk6.20031', 'vk6.20038', 'vk6.20039', 'vk6.20101', 'vk6.20103', 'vk6.20108', 'vk6.20110', 'vk6.20308', 'vk6.20309', 'vk6.20310', 'vk6.20311', 'vk6.20381', 'vk6.20382', 'vk6.20383', 'vk6.20384', 'vk6.20557', 'vk6.20564', 'vk6.20565', 'vk6.20637', 'vk6.20638', 'vk6.20639', 'vk6.20640', 'vk6.21302', 'vk6.21303', 'vk6.21319', 'vk6.21320', 'vk6.21379', 'vk6.21381', 'vk6.21387', 'vk6.21388', 'vk6.21643', 'vk6.21644', 'vk6.21647', 'vk6.21648', 'vk6.21722', 'vk6.21724', 'vk6.21725', 'vk6.21727', 'vk6.21958', 'vk6.21969', 'vk6.21970', 'vk6.22066', 'vk6.22067', 'vk6.22068', 'vk6.22069', 'vk6.22697', 'vk6.22798', 'vk6.23439', 'vk6.23441', 'vk6.23452', 'vk6.23741', 'vk6.23742', 'vk6.23751', 'vk6.24557', 'vk6.24732', 'vk6.24734', 'vk6.24735', 'vk6.24737', 'vk6.24976', 'vk6.25144', 'vk6.25147', 'vk6.27080', 'vk6.27081', 'vk6.27098', 'vk6.27099', 'vk6.27174', 'vk6.27176', 'vk6.27188', 'vk6.27190', 'vk6.27603', 'vk6.27604', 'vk6.27607', 'vk6.27608', 'vk6.27701', 'vk6.27702', 'vk6.27705', 'vk6.27706', 'vk6.28013', 'vk6.28026', 'vk6.28027', 'vk6.28121', 'vk6.28122', 'vk6.28125', 'vk6.28126', 'vk6.28783', 'vk6.28784', 'vk6.28793', 'vk6.28794', 'vk6.28857', 'vk6.28859', 'vk6.28872', 'vk6.28873', 'vk6.29155', 'vk6.29156', 'vk6.29157', 'vk6.29158', 'vk6.29245', 'vk6.29247', 'vk6.29250', 'vk6.29252', 'vk6.29479', 'vk6.29486', 'vk6.29487', 'vk6.34668', 'vk6.35515', 'vk6.35517', 'vk6.35526', 'vk6.35528', 'vk6.35963', 'vk6.35964', 'vk6.35976', 'vk6.35978', 'vk6.36698', 'vk6.36859', 'vk6.36861', 'vk6.36864', 'vk6.36866', 'vk6.37322', 'vk6.37328', 'vk6.38476', 'vk6.38477', 'vk6.38482', 'vk6.38483', 'vk6.38585', 'vk6.38587', 'vk6.38600', 'vk6.38602', 'vk6.39029', 'vk6.39030', 'vk6.39031', 'vk6.39032', 'vk6.39139', 'vk6.39141', 'vk6.39146', 'vk6.39148', 'vk6.39425', 'vk6.39426', 'vk6.39431', 'vk6.39432', 'vk6.39553', 'vk6.39554', 'vk6.39555', 'vk6.39556', 'vk6.40667', 'vk6.40668', 'vk6.40679', 'vk6.40680', 'vk6.40773', 'vk6.40775', 'vk6.40788', 'vk6.40789', 'vk6.41280', 'vk6.41281', 'vk6.41284', 'vk6.41285', 'vk6.41619', 'vk6.41620', 'vk6.41627', 'vk6.41628', 'vk6.41779', 'vk6.41780', 'vk6.41781', 'vk6.41782', 'vk6.42325', 'vk6.42933', 'vk6.42935', 'vk6.42940', 'vk6.42942', 'vk6.43228', 'vk6.43229', 'vk6.43235', 'vk6.43237', 'vk6.43974', 'vk6.44085', 'vk6.44087', 'vk6.44088', 'vk6.44090', 'vk6.45361', 'vk6.45362', 'vk6.45373', 'vk6.45374', 'vk6.45469', 'vk6.45471', 'vk6.45476', 'vk6.45478', 'vk6.45875', 'vk6.45877', 'vk6.45878', 'vk6.45880', 'vk6.46004', 'vk6.46005', 'vk6.46014', 'vk6.46015', 'vk6.46163', 'vk6.46164', 'vk6.46167', 'vk6.46168', 'vk6.47126', 'vk6.47127', 'vk6.47132', 'vk6.47133', 'vk6.47205', 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'vk6.83250', 'vk6.83254', 'vk6.83260', 'vk6.83264', 'vk6.83267', 'vk6.83273', 'vk6.83281', 'vk6.83287', 'vk6.83289', 'vk6.83299', 'vk6.83301', 'vk6.83307', 'vk6.83309', 'vk6.83409', 'vk6.83415', 'vk6.83434', 'vk6.83439', 'vk6.83453', 'vk6.83457', 'vk6.83520', 'vk6.83523', 'vk6.83525', 'vk6.83529', 'vk6.83643', 'vk6.83645', 'vk6.83656', 'vk6.83658', 'vk6.83711', 'vk6.83715', 'vk6.83717', 'vk6.83719', 'vk6.83721', 'vk6.83743', 'vk6.83745', 'vk6.83870', 'vk6.83873', 'vk6.83874', 'vk6.83877', 'vk6.83879', 'vk6.83881', 'vk6.83884', 'vk6.83885', 'vk6.83988', 'vk6.84025', 'vk6.84028', 'vk6.84102', 'vk6.84106', 'vk6.84115', 'vk6.84119', 'vk6.84254', 'vk6.84257', 'vk6.84264', 'vk6.84268', 'vk6.84449', 'vk6.84553', 'vk6.84647', 'vk6.84770', 'vk6.84773', 'vk6.84774', 'vk6.84780', 'vk6.84783', 'vk6.84785', 'vk6.84788', 'vk6.84904', 'vk6.84907', 'vk6.84908', 'vk6.84911', 'vk6.84952', 'vk6.84955', 'vk6.84959', 'vk6.84962', 'vk6.85094', 'vk6.85097', 'vk6.85176', 'vk6.85180', 'vk6.85182', 'vk6.85186', 'vk6.85199', 'vk6.85203', 'vk6.85206', 'vk6.85210', 'vk6.85282', 'vk6.85286', 'vk6.85290', 'vk6.85292', 'vk6.85326', 'vk6.85330', 'vk6.85340', 'vk6.85344', 'vk6.85390', 'vk6.85394', 'vk6.85404', 'vk6.85530', 'vk6.85532', 'vk6.85692', 'vk6.85695', 'vk6.85697', 'vk6.85807', 'vk6.85811', 'vk6.86026', 'vk6.86032', 'vk6.86034', 'vk6.86040', 'vk6.86058', 'vk6.86059', 'vk6.86063', 'vk6.86065', 'vk6.86068', 'vk6.86073', 'vk6.86077', 'vk6.86079', 'vk6.86092', 'vk6.86095', 'vk6.86101', 'vk6.86103', 'vk6.86112', 'vk6.86122', 'vk6.86126', 'vk6.86132', 'vk6.86135', 'vk6.86137', 'vk6.86143', 'vk6.86145', 'vk6.86150', 'vk6.86153', 'vk6.86158', 'vk6.86161', 'vk6.86269', 'vk6.86271', 'vk6.86289', 'vk6.86294', 'vk6.86331', 'vk6.86333', 'vk6.86337', 'vk6.86356', 'vk6.86571', 'vk6.86573', 'vk6.86588', 'vk6.86590', 'vk6.86642', 'vk6.86649', 'vk6.86651', 'vk6.86657', 'vk6.86659', 'vk6.86712', 'vk6.86714', 'vk6.86772', 'vk6.86773', 'vk6.86782', 'vk6.86783', 'vk6.86788', 'vk6.86789', 'vk6.86792', 'vk6.86793', 'vk6.86796', 'vk6.86797', 'vk6.86806', 'vk6.86807', 'vk6.86812', 'vk6.86813', 'vk6.86862', 'vk6.86865', 'vk6.86870', 'vk6.86873', 'vk6.86972', 'vk6.86975', 'vk6.86980', 'vk6.86983', 'vk6.87004', 'vk6.87007', 'vk6.87012', 'vk6.87015', 'vk6.87100', 'vk6.87103', 'vk6.87108', 'vk6.87111', 'vk6.87271', 'vk6.87405', 'vk6.87410', 'vk6.87419', 'vk6.87425', 'vk6.87444', 'vk6.87447', 'vk6.87452', 'vk6.87455', 'vk6.87468', 'vk6.87471', 'vk6.87474', 'vk6.87477', 'vk6.87486', 'vk6.87513', 'vk6.87514', 'vk6.87521', 'vk6.87522', 'vk6.87782', 'vk6.87801', 'vk6.87816', 'vk6.87819', 'vk6.87822', 'vk6.87832', 'vk6.87833', 'vk6.87835', 'vk6.87838', 'vk6.87860', 'vk6.87861', 'vk6.87935', 'vk6.87938', 'vk6.87943', 'vk6.87946', 'vk6.88021', 'vk6.88024', 'vk6.88025', 'vk6.88028', 'vk6.88063', 'vk6.88066', 'vk6.88071', 'vk6.88074', 'vk6.88110', 'vk6.88238', 'vk6.88245', 'vk6.88291', 'vk6.88294', 'vk6.88305', 'vk6.88309', 'vk6.88316', 'vk6.88322', 'vk6.88331', 'vk6.88336', 'vk6.88396', 'vk6.88469', 'vk6.88542', 'vk6.88545', 'vk6.88548', 'vk6.88549', 'vk6.88552', 'vk6.88562', 'vk6.88566', 'vk6.88568', 'vk6.88609', 'vk6.88612', 'vk6.88617', 'vk6.88620', 'vk6.88861', 'vk6.88862', 'vk6.88869', 'vk6.88870', 'vk6.88884', 'vk6.88887', 'vk6.88888', 'vk6.88891', 'vk6.88951', 'vk6.88958', 'vk6.88966', 'vk6.89031', 'vk6.89034', 'vk6.89035', 'vk6.89038', 'vk6.89065', 'vk6.89067', 'vk6.89134', 'vk6.89137', 'vk6.89138', 'vk6.89141', 'vk6.89151', 'vk6.89159', 'vk6.89162', 'vk6.89231', 'vk6.89232', 'vk6.89293', 'vk6.89297', 'vk6.89305', 'vk6.89307', 'vk6.89332', 'vk6.89523', 'vk6.89526', 'vk6.89538', 'vk6.89542', 'vk6.89572', 'vk6.89575', 'vk6.89577', 'vk6.89659', 'vk6.89664', 'vk6.89668', 'vk6.89670', 'vk6.89683', 'vk6.89687', 'vk6.89698', 'vk6.89702', 'vk6.89732', 'vk6.89734', 'vk6.89750', 'vk6.89752', 'vk6.89777', 'vk6.89779', 'vk6.89787', 'vk6.89791', 'vk6.89800', 'vk6.89801', 'vk6.89803', 'vk6.89806', 'vk6.89826', 'vk6.89843', 'vk6.89844', 'vk6.89896', 'vk6.89898', 'vk6.89900', 'vk6.89906', 'vk6.89924', 'vk6.89927', 'vk6.89932', 'vk6.89935', 'vk6.89945', 'vk6.89946', 'vk6.89953', 'vk6.89988', 'vk6.89989', 'vk6.89993', 'vk6.89995', 'vk6.89998', 'vk6.90003', 'vk6.90011', 'vk6.90014', 'vk6.90015', 'vk6.90018', 'vk6.90023', 'vk6.90027', 'vk6.90028', 'vk6.90031', 'vk6.90045', 'vk6.90049']

The R3 orbit of minmal crossing diagrams contains:

The diagrammatic symmetry type of this knot is +.

The reverse -K is

The reversed mirror image -K* is

The fillings (up to the first 10) associated to the algebraic genus:

Or click here to check the fillings

invariant	value
Gauss code	O1O2O3O4U1U2U4U3
R3 orbit	{'O1O2O3O4U1U2U4U3'}
R3 orbit length	1
Gauss code of -K	O1O2O3O4U2U1U3U4
Gauss code of K*	Same
Gauss code of -K*	O1O2O3O4U2U1U3U4
Diagrammatic symmetry type	+
Flat genus of the diagram	2
If K is checkerboard colorable	False
If K is almost classical	False
Based matrix from Gauss code	[[ 0 -3 -1 2 2],[ 3 0 1 3 2],[ 1 -1 0 2 1],[-2 -3 -2 0 0],[-2 -2 -1 0 0]]
Primitive based matrix	[[ 0 2 2 -1 -3],[-2 0 0 -1 -2],[-2 0 0 -2 -3],[ 1 1 2 0 -1],[ 3 2 3 1 0]]
If based matrix primitive	True
Phi of primitive based matrix	[-2,-2,1,3,0,1,2,2,3,1]
Phi over symmetry	[-3,-1,2,2,1,2,3,1,2,0]
Phi of -K	[-3,-1,2,2,1,2,3,1,2,0]
Phi of K*	[-2,-2,1,3,0,1,2,2,3,1]
Phi of -K*	[-3,-1,2,2,1,2,3,1,2,0]
Symmetry type of based matrix	+
u-polynomial	t^3-2t^2+t
Normalized Jones-Krushkal polynomial	z+3
Enhanced Jones-Krushkal polynomial	-4w^3z+5w^2z+3w
Inner characteristic polynomial	t^4+19t^2+1
Outer characteristic polynomial	t^5+37t^3+11t
Flat arrow polynomial	-2K1K2 + K1 + K3 + 1
2-strand cable arrow polynomial	-128K12K2*2 + 48K1*2K2 - 88K12 + 64K1K23K3 + 224K1K2K3 + 16K1K3K4 - 32K24 - 64K2*2K3*2 - 8K2*2K4*2 + 8K2*2K4 - 54K22 + 16K2K3K5 + 8K2K4K6 - 88K3*2 - 12K4*2 - 2K6**2 + 90
Genus of based matrix	1
Fillings of based matrix	[[{1, 4}, {2, 3}], [{2, 4}, {1, 3}], [{3, 4}, {1, 2}], [{3, 4}, {2}, {1}]]
If K is slice	False

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