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ec_curvedata • Show schema
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{'Ciso': '7744bb', 'Clabel': '7744bb1', 'Cnumber': 1, 'abc_quality': 0.9461121308337243, 'absD': 3838050304, 'adelic_genus': 16, 'adelic_index': 480, 'adelic_level': 88, 'ainvs': [0, -1, 0, -161, 3137], 'analytic_rank': 1, 'bad_primes': [2, 11], 'class_deg': 11, 'class_size': 2, 'cm': 0, 'conductor': 7744, 'degree': 3072, 'elladic_images': ['4.4.0.3', '11.60.1.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.52175993272423887474090872434', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1, 11], 'jinv': [-121, 1], 'lmfdb_iso': '7744.bf', 'lmfdb_label': '7744.bf2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -2, -7], 'min_quad_twist_disc': -8, 'modell_images': ['11B.10.4'], 'modm_images': ['4.4.0-4.a.1.1', '11.60.1.b.1', '44.240.6-44.b.1.3', '88.480.16.?'], 'nonmax_primes': [2, 11], 'nonmax_rad': 22, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.4138142475131737483108104414', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3172592623818026040722539838', 'prec': 103}, 'szpiro_ratio': 3.304490124237855, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 2, 0, -1, 0, 2, 0, 1, 0, 0, 0, -1, 0, -2, 0, -5, 0, 6, 0], 'aplist': [0, 2, -1, 2, 0, -1, -5, 6, -2, -9, 2, 3, -5, 0, -2, -9, 8, -6, 2, -12, -2, 10, 6, -9, -13], 'class_deg': 11, 'class_size': 2, 'conductor': 7744, 'isogeny_matrix': [[1, 11], [11, 1]], 'lmfdb_iso': '7744.bf', 'trace_hash': 2205161503892129177}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.35221275602447523833826452672', 'prec': 103}, 'conductor': 7744, 'gens': [[7, 48, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.4138142475131737483108104414', 'prec': 100}], 'lmfdb_label': '7744.bf2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.1958154728733869709892648468', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7729528516369692124411268551402031439', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [7]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': [5, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '7744.bf2'}
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ec_torsion_growth • Show schema
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id: 405353
{'degree': 3, 'field': [2, 4, -1, 1], 'lmfdb_label': '7744.bf2', 'torsion': [2]}
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id: 405354
{'degree': 6, 'field': [4, 0, 20, 0, -7, 0, 1], 'lmfdb_label': '7744.bf2', 'torsion': [2, 2]}
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id: 405355
{'degree': 8, 'field': [-48, 0, -152, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '7744.bf2', 'torsion': [3]}
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id: 405356
{'degree': 10, 'field': [-352, 0, 880, 0, -616, 0, 176, 0, -22, 0, 1], 'lmfdb_label': '7744.bf2', 'torsion': [11]}
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id: 405357
{'degree': 12, 'field': [-4, 12, 35, 2, -49, 4, 16, 12, -12, -8, 13, -6, 1], 'lmfdb_label': '7744.bf2', 'torsion': [4]}
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ec_localdata • Show schema
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id: 159920
{'conductor': 7744, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '7744.bf2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 159921
{'conductor': 7744, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '7744.bf2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1715105
{'adelic_gens': [[1, 84, 0, 1], [73, 0, 0, 49], [45, 44, 44, 45], [1, 0, 44, 1], [45, 22, 22, 1], [12, 55, 77, 23], [1, 44, 0, 1], [43, 55, 0, 21], [43, 44, 22, 87]], 'adelic_image': '88.480.16.?', 'conductor': 7744, 'lmfdb_label': '7744.bf2', 'prime': 0}
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id: 37936
{'conductor': 7744, 'elladic_image': '4.4.0.3', 'lmfdb_label': '7744.bf2', 'modell_image': '2G', 'prime': 2}
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id: 37937
{'conductor': 7744, 'elladic_image': '11.60.1.4', 'lmfdb_label': '7744.bf2', 'modell_image': '11B.10.4', 'prime': 11}
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ec_padic • Show schema
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id: 316418
{'lmfdb_iso': '7744.bf', 'p': 5, 'prec': 20, 'unit': 156993335584, 'val': 3}
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id: 316419
{'lmfdb_iso': '7744.bf', 'p': 7, 'prec': 20, 'unit': 2368805387764317, 'val': 1}
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id: 316424
{'lmfdb_iso': '7744.bf', 'p': 13, 'prec': 20, 'unit': 869373836700791972276, 'val': 1}
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id: 316426
{'lmfdb_iso': '7744.bf', 'p': 17, 'prec': 20, 'unit': 177381154392035989077733, 'val': 1}
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id: 316427
{'lmfdb_iso': '7744.bf', 'p': 19, 'prec': 20, 'unit': 1342099077113937945290456, 'val': 1}
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id: 316431
{'lmfdb_iso': '7744.bf', 'p': 23, 'prec': 20, 'unit': 67270558213108771511573816, 'val': 1}
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id: 316423
{'lmfdb_iso': '7744.bf', 'p': 29, 'prec': 20, 'unit': 909247978642722361190889694, 'val': 1}
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id: 316420
{'lmfdb_iso': '7744.bf', 'p': 31, 'prec': 20, 'unit': 1920452343143135598346965140, 'val': 1}
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id: 316435
{'lmfdb_iso': '7744.bf', 'p': 37, 'prec': 20, 'unit': 375065392067655038300055434143, 'val': 1}
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id: 316421
{'lmfdb_iso': '7744.bf', 'p': 41, 'prec': 20, 'unit': 1835733182869209828266674449898, 'val': 1}
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id: 316433
{'lmfdb_iso': '7744.bf', 'p': 47, 'prec': 20, 'unit': 34524135102804667707148553908569, 'val': 1}
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id: 316428
{'lmfdb_iso': '7744.bf', 'p': 53, 'prec': 20, 'unit': 495418753386517262371378975999735, 'val': 1}
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id: 316429
{'lmfdb_iso': '7744.bf', 'p': 59, 'prec': 20, 'unit': 1659507853786032866214617090356770, 'val': 1}
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id: 316434
{'lmfdb_iso': '7744.bf', 'p': 61, 'prec': 20, 'unit': 5456004628518236146183780402553905, 'val': 1}
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id: 316417
{'lmfdb_iso': '7744.bf', 'p': 67, 'prec': 20, 'unit': 39624916644989207922283357677819455, 'val': 1}
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id: 316422
{'lmfdb_iso': '7744.bf', 'p': 71, 'prec': 20, 'unit': 11935060290713851173555962440678866, 'val': 1}
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id: 316430
{'lmfdb_iso': '7744.bf', 'p': 73, 'prec': 20, 'unit': 199847031344574007871419106721167559, 'val': 1}
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id: 316425
{'lmfdb_iso': '7744.bf', 'p': 79, 'prec': 20, 'unit': 14094826321782399890215542773148695, 'val': 1}
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id: 316416
{'lmfdb_iso': '7744.bf', 'p': 83, 'prec': 20, 'unit': 550177250138508916183339810688113516, 'val': 1}
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id: 316432
{'lmfdb_iso': '7744.bf', 'p': 89, 'prec': 20, 'unit': 6295643048526999302360926817360474102, 'val': 1}
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id: 316415
{'lmfdb_iso': '7744.bf', 'p': 97, 'prec': 20, 'unit': 21081953742706688905739653006416158525, 'val': 1}