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ec_curvedata • Show schema
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{'Ciso': '7728p', 'Clabel': '7728p1', 'Cnumber': 1, 'abc_quality': 1.0015555607612345, 'absD': 417391501715177472, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1288, 'ainvs': [0, 1, 0, -235912, -54035212], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 7728, 'degree': 101376, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0960554569704814311127848778', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2], 'jinv': [-354499561600764553, 101902222098432], 'lmfdb_iso': '7728.t', 'lmfdb_label': '7728.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -14744, 836928], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '14.6.0.b.1', '184.6.0.?', '1288.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.2881994304432057143107264422', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4029082764105361216955527563', 'prec': 100}, 'szpiro_ratio': 5.487846686898397, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 2, 0, -1, 0, 1, 0, 4, 0, -4, 0, 2, 0, -4, 0, 2, 0], 'aplist': [0, 1, 2, -1, 4, -4, -4, 2, -1, -6, -6, -2, -10, -8, -10, -6, 12, -10, -8, 4, -2, 8, 6, 0, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 7728, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '7728.t', 'trace_hash': 1784658460338913222}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.015114346091024609994300387893', 'prec': 107}, 'conductor': 7728, 'gens': [[1724, 68310, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.2881994304432057143107264422', 'prec': 100}], 'lmfdb_label': '7728.t2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10672624536816712913070997143', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6149948677271836154629967265015574960', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[574, 0, 1]], 'xcoord_integral_points': [574, 1724]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '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, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '7728.t2'}
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ec_torsion_growth • Show schema
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id: 404336
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '7728.t2', 'torsion': [2, 2]}
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id: 404337
{'degree': 4, 'field': [-175, 0, 6, 0, 1], 'lmfdb_label': '7728.t2', 'torsion': [4]}
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id: 404340
{'degree': 8, 'field': [-15552, 0, 720, 0, -432, 0, 0, 0, 1], 'lmfdb_label': '7728.t2', 'torsion': [6]}
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id: 404338
{'degree': 8, 'field': [81, 81, 72, 33, 26, -11, 8, -3, 1], 'lmfdb_label': '7728.t2', 'torsion': [2, 4]}
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id: 404339
{'degree': 8, 'field': [33688, -1552, 1292, 500, -199, -64, 26, -4, 1], 'lmfdb_label': '7728.t2', 'torsion': [2, 4]}
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id: 404342
{'degree': 16, 'field': [33628401, 0, 2431344, 0, 2092876, 0, 318624, 0, 61014, 0, 2672, 0, 492, 0, 0, 0, 1], 'lmfdb_label': '7728.t2', 'torsion': [2, 6]}
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id: 404341
{'degree': 16, 'field': [95646852, -66418272, 70440480, -8148448, 4391996, -537760, 424568, -179104, 4877, 28440, -8196, 2200, -1034, 280, -20, -8, 1], 'lmfdb_label': '7728.t2', 'torsion': [8]}
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ec_localdata • Show schema
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id: 159534
{'conductor': 7728, 'conductor_valuation': 4, 'discriminant_valuation': 34, 'j_denominator_valuation': 22, 'kodaira_symbol': -30, 'lmfdb_label': '7728.t2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 159535
{'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '7728.t2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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id: 159536
{'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.t2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 159537
{'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7728.t2', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1715016
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [281, 4, 562, 9], [809, 484, 160, 1127], [1, 4, 0, 1], [370, 1, 1103, 0], [1285, 4, 1284, 5], [645, 4, 2, 9]], 'adelic_image': '1288.12.0.?', 'conductor': 7728, 'lmfdb_label': '7728.t2', 'prime': 0}
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id: 37892
{'conductor': 7728, 'elladic_image': '2.3.0.1', 'lmfdb_label': '7728.t2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 315397
{'lmfdb_iso': '7728.t', 'p': 5, 'prec': 20, 'unit': 15460328454288, 'val': 1}
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id: 315396
{'lmfdb_iso': '7728.t', 'p': 11, 'prec': 20, 'unit': 13986493782952927506, 'val': 1}
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id: 315403
{'lmfdb_iso': '7728.t', 'p': 13, 'prec': 20, 'unit': 326447445186615498000, 'val': 1}
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id: 315405
{'lmfdb_iso': '7728.t', 'p': 17, 'prec': 20, 'unit': 206231754065505616455372, 'val': 1}
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id: 315406
{'lmfdb_iso': '7728.t', 'p': 19, 'prec': 20, 'unit': 1348952768790319348529922, 'val': 1}
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id: 315402
{'lmfdb_iso': '7728.t', 'p': 29, 'prec': 20, 'unit': 1155345162498207737772112619, 'val': 1}
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id: 315399
{'lmfdb_iso': '7728.t', 'p': 31, 'prec': 20, 'unit': 13296192584794997706348371787, 'val': 1}
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id: 315413
{'lmfdb_iso': '7728.t', 'p': 37, 'prec': 20, 'unit': 380094921393978744681198061283, 'val': 1}
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id: 315400
{'lmfdb_iso': '7728.t', 'p': 41, 'prec': 20, 'unit': 1069908067206920085877952561351, 'val': 1}
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id: 315401
{'lmfdb_iso': '7728.t', 'p': 43, 'prec': 20, 'unit': 5795814221977378412591812073781, 'val': 1}
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id: 315411
{'lmfdb_iso': '7728.t', 'p': 47, 'prec': 20, 'unit': 2216579546493301778523575103488, 'val': 1}
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id: 315407
{'lmfdb_iso': '7728.t', 'p': 53, 'prec': 20, 'unit': 118036285017422338593474762858485, 'val': 1}
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id: 315408
{'lmfdb_iso': '7728.t', 'p': 59, 'prec': 20, 'unit': 3000884874135045474909017236213750, 'val': 1}
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id: 315412
{'lmfdb_iso': '7728.t', 'p': 61, 'prec': 20, 'unit': 838883458110425724324949267822927, 'val': 1}
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id: 315395
{'lmfdb_iso': '7728.t', 'p': 67, 'prec': 20, 'unit': 17844044003971788571006404978792004, 'val': 1}
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id: 315398
{'lmfdb_iso': '7728.t', 'p': 71, 'prec': 20, 'unit': 128379816882834901977136563747675231, 'val': 1}
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id: 315409
{'lmfdb_iso': '7728.t', 'p': 73, 'prec': 20, 'unit': 121159542016295888518965307226015114, 'val': 1}
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id: 315404
{'lmfdb_iso': '7728.t', 'p': 79, 'prec': 20, 'unit': 456986266254565728645982213406535400, 'val': 1}
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id: 315410
{'lmfdb_iso': '7728.t', 'p': 83, 'prec': 20, 'unit': 1870469623412108119898478408467347252, 'val': 1}
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id: 315394
{'lmfdb_iso': '7728.t', 'p': 97, 'prec': 20, 'unit': 41912329771596765022864676458842120110, 'val': 1}