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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, 5, 36], [0, 1, 47, 34], [0, 1, 47, 50], [0, 3, 25, 50], [0, 5, 19, 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.1', 'coarse_level': 56, 'coarse_num': 1, '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': [[38, 81, 57, 110], [63, 50, 58, 23], [80, 3, 7, 92], [93, 78, 84, 87], [97, 82, 94, 45]], '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.1.1', '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.1.6'], '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.1'], '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': '56.24.0.119', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 7], 'canonical_conjugator': [43, 28, 28, 1], 'canonical_generators': [[0, 1, 5, 36], [0, 1, 47, 34], [0, 1, 47, 50], [0, 3, 25, 50], [0, 5, 19, 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.1', 'coarse_level': 56, 'coarse_num': 1, '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': [[36, 39, 47, 4], [45, 14, 44, 43], [45, 48, 32, 5], [47, 26, 48, 29], [50, 39, 13, 16]], '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.1', '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.1'], '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': [[7, 8, 5, 15]], '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.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': ['(7*x+y)^24*(62121073*x^8-51323776*x^7*y-226174200*x^6*y^2-160864256*x^5*y^3+61244120*x^4*y^4+183318016*x^3*y^5+109082400*x^2*y^6+22378496*x*y^7+1811728*y^8)^3', '(x+2*y)^4*(7*x+y)^26*(7*x^2-2*y^2)^8*(42*x^2-14*x*y-27*y^2)'], 'degree': 24, 'domain_label': '56.24.0.bu.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-2^2', '7^2*13^8'], 'upload_id': None}
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modcurve_points • Show schema
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id: 1460
{'Elabel': '42.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 42, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 33.2238660985887, 'jinv': '268498407453697/252', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 1848663
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-2:1', '-1/7:1']}, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', '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: 599
{'Elabel': '21.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 21, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 31.6069098121035, 'jinv': '53297461115137/147', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 4088
{'Elabel': '210.e8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 33.2263458355123, 'jinv': '226523624554079/269165039062500', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 10189
{'Elabel': '840.d5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 840, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 21.119878434283, 'jinv': '1486779836/8203125', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 10222
{'Elabel': '840.f1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 840, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 34.2960402637348, 'jinv': '784478485879202/221484375', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 10388
{'Elabel': '840.j2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 840, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 30.3185657316219, 'jinv': '14695548366242/57421875', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 13033
{'Elabel': '1155.f3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1155, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 48.0720936147162, 'jinv': '-754127868744065783521/15825714261328125', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 14467
{'Elabel': '1302.j4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1302, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 43.4587961723848, 'jinv': '7480237168421652097/3438856662962112', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 18721
{'Elabel': '1848.g6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1848, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 32.6156043863813, 'jinv': '146142660369886/94532266521', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 21336
{'Elabel': '2184.c4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2184, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 36.2979031262268, 'jinv': '5807363790481348/1079211743883', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 21426
{'Elabel': '2184.j3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2184, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 31.1760128792428, 'jinv': '-34639400027234/17130345141', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 25783
{'Elabel': '2730.w6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2730, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 44.4539563341879, 'jinv': '-4047051964543660801/20235220197806250000', 'jorig': '-4047051964543660801/20235220197806250000', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 29284
{'Elabel': '3255.d6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 3255, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 44.1181935669239, 'jinv': '14463986828816730239/11194194866413125', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 33405
{'Elabel': '3990.s4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 3990, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 47.2531763358439, 'jinv': '332501596620668284321/3896484375000000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 42690
{'Elabel': '5565.b1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 5565, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 60.7527134641884, 'jinv': '242419872314743996084037281/371418914794921875', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 48680
{'Elabel': '6510.r2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 6510, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 55.9644721901598, 'jinv': '2018651992700195476824481/75097045898437500', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 60510
{'Elabel': '8778.q3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 8778, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 57.3849486760949, 'jinv': '-8355386696649362939743777/2053401528143312730768', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 63258
{'Elabel': '9240.r4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 9240, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 38.6720343446517, 'jinv': '62380825826921284/787768887675', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 63464
{'Elabel': '9240.bi1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 9240, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 47.0005993479244, 'jinv': '258286045443018193442/8440380939375', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 66437
{'Elabel': '9870.p2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 9870, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 66.1115901295151, 'jinv': '51510857911263182185075707841/345625588152793267200', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 89640
{'Elabel': '15015.i1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 15015, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 77.8045753155721, 'jinv': '6167337657175608278710367816539201/124974906951542660615277675', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 93190
{'Elabel': '15834.s1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 15834, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 77.550846112757, 'jinv': '4785248917621471258548792495897697/435894213304313439033688512', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 93737
{'Elabel': '15960.c2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 15960, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 40.9668896034519, 'jinv': '619004912314743364/3273046875', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 106209
{'Elabel': '18753.a4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 18753, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '56.24.0.bu.1', 'curve_level': 56, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 43.7033161317486, 'jinv': '-9552323829803864257/256518991207151253', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 126045
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