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gps_gl2zhat_fine • Show schema
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{'CPlabel': '4E0', 'Glabel': None, 'RSZBlabel': '68.12.0.15', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 17], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 4, 1], [1, 0, 34, 1], [1, 2, 7, 51], [1, 2, 52, 55], [1, 4, 0, 1], [1, 4, 29, 51], [5, 4, 64, 65], [35, 0, 34, 35]], 'cm_discriminants': [-4], 'coarse_class': '68.12.0.k', 'coarse_class_num': 11, 'coarse_index': 12, 'coarse_label': '68.12.0.k.1', 'coarse_level': 68, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 2]], 'cusp_widths': [[2, 2], [4, 2]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[1, 0, 27, 7], [45, 16, 9, 23], [51, 26, 60, 21]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 12, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [17, 18, 1], [34, 18, 1], [34, 36, 1], [68, 36, 1], [68, 72, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [17, 144, 1], [34, 144, 1], [34, 288, 1], [68, 576, 1], [68, 1152, 1]], 'label': '68.12.0.k.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.e.1', '34.2.0.a.1', '34.6.0.a.1', '68.6.0.b.1', '68.12.0.k.1'], 'lattice_x': [3350, 5370, 5123, 1330, 1576, 8670, 5123], 'level': 68, 'level_is_squarefree': False, 'level_radical': 34, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 19, 'num_known_degree1_noncusp_points': 19, 'num_known_degree1_points': 20, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [17, 288, 1], [34, 288, 1], [34, 576, 1], [68, 1152, 1], [68, 2304, 1]], 'parents': ['4.6.0.e.1', '34.6.0.a.1', '68.6.0.b.1'], 'parents_conj': [[60, 51, 67, 22], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': None, 'psl2index': 12, 'psl2label': '4.12.0.a.1', 'psl2level': 4, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.e.1', '34.6.0.a.1'], 'scalar_label': '1.1.1', 'simple': None, 'sl2label': '4.12.0.a.1', 'sl2level': 4, 'squarefree': None, 'trace_hash': 0, 'traces': []}
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modcurve 68.12.0.k.1 does not appear in modcurve_models
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modcurve_modelmaps • Show schema
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{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['(x-6*y)^12*(11*x^2-68*x*y+1292*y^2)^3*(15*x^2+204*x*y+1564*y^2)^3', '(x-6*y)^12*(x^2+68*x*y+68*y^2)^4*(13*x^2+68*x*y+1428*y^2)^2'], 'degree': 12, 'domain_label': '68.12.0.k.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^4', '1'], 'upload_id': None}
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modcurve_points • Show schema
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id: 1848803
{'Elabel': None, 'ainvs': None, 'cardinality': 0, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['6:1']}, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': True, 'degree': 1, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 10578
{'Elabel': '867.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 867, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 12.5231618096869, 'jinv': '274625/81', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 33808
{'Elabel': '4046.n1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 4046, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 23.0126844940864, 'jinv': '9869198625/614656', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 73021
{'Elabel': '11271.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 11271, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 39.5347392682559, 'jinv': '147815204204011553/15178486401', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 102689
{'Elabel': '17918.b1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 17918, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 41.1945112608939, 'jinv': '777228872334890625/60523872256', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 107511
{'Elabel': '19074.s1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 19074, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 20.7973436747175, 'jinv': '1076890625/17424', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 107530
{'Elabel': '19074.y1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 19074, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 34.0197492356957, 'jinv': '595099203230897/5780865024', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 150483
{'Elabel': '30056.f1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 30056, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 18.0904251439415, 'jinv': '71874000/169', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 191679
{'Elabel': '41327.e1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 41327, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 28.1621942972851, 'jinv': '1700926633953/418161601', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 209222
{'Elabel': '46529.b1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 46529, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 30.4865738377467, 'jinv': '17384043092625/25921', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 215751
{'Elabel': '48552.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 48552, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 21.0123883075266, 'jinv': '1335255248/441', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 225295
{'Elabel': '51442.f1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 51442, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 26.5165254402939, 'jinv': '328080696273/32444416', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 312066
{'Elabel': '79186.g1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 79186, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 29.5096384403467, 'jinv': '6544449752625/300304', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 440608
{'Elabel': '125137.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 125137, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 36.4241703420708, 'jinv': '6588949628792817/187489', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 524562
{'Elabel': '157794.bt1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 157794, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 32.9120855091814, 'jinv': '196579001398625/78149320704', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 582285
{'Elabel': '181203.f1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 181203, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 70.73247371868, 'jinv': '5232666152934469558176256390625/294886783077799086801', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 663376
{'Elabel': '215016.c1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 215016, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 43.151516016194, 'jinv': '5501299528845794000/700569', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 691628
{'Elabel': '227154.k1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 227154, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 35.8378810304724, 'jinv': '3666012780227057/39538944', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 749646
{'Elabel': '252586.k1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 252586, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 37.3674224807926, 'jinv': '16922533650107553/583506543376', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 865464
{'Elabel': '305184.n1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 305184, 'coordinates': None, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '68.12.0.k.1', 'curve_level': 68, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 29.2961227512195, 'jinv': '5286210488000/1089', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}