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gps_gl2zhat_fine • Show schema
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{'CPlabel': '8I0', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 7], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[0, 1, 47, 34], [0, 1, 47, 50], [0, 3, 39, 36], [0, 5, 19, 50], [0, 15, 5, 50], [8, 7, 49, 22], [8, 49, 7, 50], [9, 8, 48, 49], [55, 0, 0, 111], [57, 56, 56, 57], [111, 0, 56, 111], [111, 0, 104, 111], [111, 56, 0, 111], [111, 104, 0, 111]], 'cm_discriminants': [], 'coarse_class': '56.24.0.bu', 'coarse_class_num': 47, 'coarse_index': 24, 'coarse_label': '56.24.0.bu.2', 'coarse_level': 56, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 2]], 'cusp_widths': [[1, 2], [2, 1], [4, 1], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 1, 'generators': [[25, 46, 76, 19], [30, 53, 59, 96], [33, 62, 40, 63], [41, 72, 26, 71], [92, 5, 69, 92]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [7, 8, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [14, 8, 1], [14, 16, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1], [28, 8, 2], [28, 32, 1], [56, 8, 2], [56, 16, 1], [56, 64, 1], [112, 16, 2], [112, 32, 1], [112, 128, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [7, 24, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [14, 24, 1], [14, 48, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [28, 48, 2], [28, 192, 1], [56, 96, 2], [56, 192, 1], [56, 768, 1], [112, 384, 2], [112, 768, 1], [112, 3072, 1]], 'label': '112.48.0-56.bu.2.1', 'lattice_labels': None, 'lattice_x': None, 'level': 112, 'level_is_squarefree': False, 'level_radical': 14, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': None, 'num_known_degree1_noncusp_points': None, 'num_known_degree1_points': None, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 2], [4, 8, 1], [7, 48, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [14, 48, 1], [14, 96, 1], [16, 8, 2], [16, 16, 1], [16, 32, 1], [16, 128, 1], [28, 96, 2], [28, 384, 1], [56, 192, 2], [56, 384, 1], [56, 1536, 1], [112, 384, 2], [112, 768, 1], [112, 1536, 1], [112, 6144, 1]], 'parents': ['16.24.0-8.n.1.8', '112.24.0-8.n.1.5'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.c.1', 'psl2level': 8, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.8', '56.24.0.bu.2'], 'scalar_label': '8.4.1', 'simple': None, 'sl2label': '8.24.0.c.1', 'sl2level': 16, 'squarefree': None, 'trace_hash': None, 'traces': None}
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gps_gl2zhat_fine • Show schema
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{'CPlabel': '8I0', 'Glabel': None, 'RSZBlabel': '56.24.0.118', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 7], 'canonical_conjugator': [29, 42, 0, 1], 'canonical_generators': [[0, 1, 47, 34], [0, 1, 47, 50], [0, 3, 39, 36], [0, 5, 19, 50], [0, 15, 5, 50], [1, 0, 8, 1], [1, 8, 0, 1], [8, 7, 49, 22], [8, 49, 7, 50], [9, 8, 48, 49]], 'cm_discriminants': [], 'coarse_class': '56.24.0.bu', 'coarse_class_num': 47, 'coarse_index': 24, 'coarse_label': '56.24.0.bu.2', 'coarse_level': 56, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 2]], 'cusp_widths': [[1, 2], [2, 1], [4, 1], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[12, 25, 9, 20], [14, 29, 19, 4], [38, 25, 7, 44], [51, 54, 12, 17], [53, 28, 0, 1]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [7, 8, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [14, 8, 1], [14, 16, 1], [28, 8, 2], [28, 32, 1], [56, 8, 2], [56, 16, 1], [56, 64, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [7, 24, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [14, 24, 1], [14, 48, 1], [28, 48, 2], [28, 192, 1], [56, 96, 2], [56, 192, 1], [56, 768, 1]], 'label': '56.24.0.bu.2', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '56.24.0.bu.2'], 'lattice_x': [5000, 5000, 5000, 5000, 5000], 'level': 56, 'level_is_squarefree': False, 'level_radical': 14, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 74, 'num_known_degree1_noncusp_points': 74, 'num_known_degree1_points': 75, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 2], [4, 8, 1], [7, 48, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [14, 48, 1], [14, 96, 1], [28, 96, 2], [28, 384, 1], [56, 192, 2], [56, 384, 1], [56, 1536, 1]], 'parents': ['8.12.0.n.1'], 'parents_conj': [[41, 34, 23, 29]], 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.c.1', 'psl2level': 8, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '4.6.0.c.1', '8.12.0.n.1'], 'scalar_label': '8.2.2', 'simple': None, 'sl2label': '8.24.0.c.1', 'sl2level': 8, 'squarefree': None, 'trace_hash': 0, 'traces': []}
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modcurve 56.24.0.bu.2 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-22*y)^24*(359*x^8-27104*x^7*y+652848*x^6*y^2-790272*x^5*y^3-91281120*x^4*y^4+1030339072*x^3*y^5-4067178752*x^2*y^6-34184708096*x*y^7+282642800384*y^8)^3', '(x-42*y)^2*(x-22*y)^24*(x-2*y)^4*(3*x^2+28*x*y-868*y^2)^8*(13*x^2+28*x*y-1708*y^2)'], 'degree': 24, 'domain_label': '56.24.0.bu.2', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^11', '7^2'], 'upload_id': None}
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modcurve_points • Show schema
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id: 630
{'Elabel': '21.a3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 21, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 22.6058901073323, 'jinv': '6570725617/45927', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 1568
{'Elabel': '42.a6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 42, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 29.48095321965, 'jinv': '6359387729183/4218578658', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 1848664
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['2:1', '22:1']}, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, '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: 3957
{'Elabel': '210.e4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 40.474991054895, 'jinv': '378499465220294881/120530818800', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 10152
{'Elabel': '840.d1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 840, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 31.7607513385192, 'jinv': '62161150998242/1607445', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 10284
{'Elabel': '840.f4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 840, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 28.6419860439199, 'jinv': '2748251600896/2205', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 10420
{'Elabel': '840.j5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 840, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 17.0311016339468, 'jinv': '-24918016/229635', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 13038
{'Elabel': '1155.f4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1155, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 42.0464291060697, 'jinv': '1821931919215868881/761147600816295', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 14448
{'Elabel': '1302.j1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1302, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 58.0346269421884, 'jinv': '15999935809592383211759617/984312', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 18713
{'Elabel': '1848.g4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1848, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 31.7604221359828, 'jinv': '62140690757632/6237', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 21326
{'Elabel': '2184.c3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2184, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 40.1767049837026, 'jinv': '-280880296871140514/25701087819771', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 21450
{'Elabel': '2184.j5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2184, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 25.2745861516242, 'jinv': '94757435392/4179357', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 25713
{'Elabel': '2730.w2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2730, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 58.2236306669175, 'jinv': '19328649688935739391016961/1048320', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 29251
{'Elabel': '3255.d1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 3255, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 48.2696073116119, 'jinv': '918806584975140864241/249153975', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 33390
{'Elabel': '3990.s3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 3990, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 47.7025046612073, 'jinv': '-521116167586355661601/1092005739697609800', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 42760
{'Elabel': '5565.b8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 5565, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 50.035039825678, 'jinv': '5369597073313118498159/6177717781067295225', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 48666
{'Elabel': '6510.r1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 6510, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 60.5807359459372, 'jinv': '204117072508351537504018561/1958536333827640350', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 60513
{'Elabel': '8778.q4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 8778, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 54.0184486736226, 'jinv': '288346165168365986554657/24161406994909400832', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 63234
{'Elabel': '9240.r1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 9240, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 47.5939486348816, 'jinv': '467508233804095622882/315748125', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 63526
{'Elabel': '9240.bi5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 9240, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 32.0690883059243, 'jinv': '84611246065664/580054565475', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 66434
{'Elabel': '9870.p1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 9870, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 69.5828308483883, 'jinv': '1657446323542297752888991143361/85350109898515796460000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 89674
{'Elabel': '15015.i5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 15015, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 66.5879399245976, 'jinv': '82942070120330816933825086799/372700833188302062975155625', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 93193
{'Elabel': '15834.s2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 15834, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 74.4945445852475, 'jinv': '225200652891919039722467527495777/779282266700773756956672', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 93767
{'Elabel': '15960.c6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 15960, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 37.7638448863337, 'jinv': '25155297018905758/48148401221235', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 106198
{'Elabel': '18753.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 18753, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.2', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 46.5259011157153, 'jinv': '160672710488355794737/352018311150807', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 126078
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