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ec_curvedata • Show schema
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{'Ciso': '76050eq', 'Clabel': '76050eq1', 'Cnumber': 1, 'abc_quality': 0.921916399763192, 'absD': 54892402671600000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1560, 'ainvs': [1, -1, 1, -1997105, 1143788897], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 76050, 'degree': 2580480, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5417620212056676684883730869', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 109, 'isogeny_degrees': [1, 2], 'jinv': [-16022066761, 998400], 'lmfdb_iso': '76050.ef', 'lmfdb_label': '76050.ef2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -52, -176], 'min_quad_twist_disc': -195, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '40.6.0.c.1', '78.6.0.?', '1560.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.68195724809170324104453196157', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.094737758076205732536372918957', 'prec': 110}, 'szpiro_ratio': 4.914741318196496, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 0, 1, 0, 0, -2, 1, 0, 0, 4, 0, 0, -2, 0, 1, 4, 0, 2, 0], 'aplist': [1, 0, 0, -2, 4, 0, 4, 2, 2, -8, -4, 6, 10, -4, 0, 6, -12, -2, -8, 0, 0, -8, 12, -10, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 76050, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '76050.ef', 'trace_hash': 1214922894513794250}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0061980283695830365243827576610', 'prec': 110}, 'conductor': 76050, 'gens': [[-341, 42420, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.68195724809170324104453196157', 'prec': 103}], 'lmfdb_label': '76050.ef2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19591940991595506656241443205', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.688692930722805868590900733154465727', 'prec': 130}, 'tamagawa_product': 320, 'torsion_generators': [[-1641, 820, 1]], 'xcoord_integral_points': [-1641, -341, 609, 1063, 3039]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 0], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 0], '13': 'a', '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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '76050.ef2'}
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ec_torsion_growth • Show schema
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id: 3596430
{'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '76050.ef2', 'torsion': [2, 2]}
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id: 3596431
{'degree': 4, 'field': [-1, -20, -4, 0, 1], 'lmfdb_label': '76050.ef2', 'torsion': [4]}
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id: 3596434
{'degree': 8, 'field': [-12454, 18642, -15392, 4849, -585, 104, 38, -3, 1], 'lmfdb_label': '76050.ef2', 'torsion': [6]}
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id: 3596433
{'degree': 8, 'field': [1600, -3200, 3320, -1800, 554, -84, 5, -2, 1], 'lmfdb_label': '76050.ef2', 'torsion': [2, 4]}
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id: 3596432
{'degree': 8, 'field': [2406, 1146, 69, -402, 181, -14, -9, -2, 1], 'lmfdb_label': '76050.ef2', 'torsion': [2, 4]}
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id: 3596435
{'degree': 16, 'field': [-7788390464, -10686257792, 433115808, 1129571552, 509195828, -56970432, 1527684, -4810104, 904353, -192512, 86416, -4560, 3078, -624, 12, -8, 1], 'lmfdb_label': '76050.ef2', 'torsion': [8]}
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id: 3596436
{'degree': 16, 'field': [107868996, 0, 111020088, 0, 17735428, 0, 2679051, 0, 468270, 0, 50911, 0, 2733, 0, 78, 0, 1], 'lmfdb_label': '76050.ef2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 1849332
{'conductor': 76050, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '76050.ef2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
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id: 1849333
{'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '76050.ef2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 1849334
{'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '76050.ef2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 1849335
{'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '76050.ef2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2166488
{'adelic_gens': [[1, 0, 4, 1], [937, 4, 314, 9], [781, 4, 2, 9], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [1042, 1, 1039, 0], [602, 1, 479, 0], [1557, 4, 1556, 5], [977, 586, 584, 975]], 'adelic_image': '1560.12.0.?', 'conductor': 76050, 'lmfdb_label': '76050.ef2', 'prime': 0}
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id: 314113
{'conductor': 76050, 'elladic_image': '2.3.0.1', 'lmfdb_label': '76050.ef2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 3915389
{'lmfdb_iso': '76050.ef', 'p': 7, 'prec': 20, 'unit': 9793695189480789, 'val': 1}
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id: 3915394
{'lmfdb_iso': '76050.ef', 'p': 11, 'prec': 20, 'unit': 20521290101792747882, 'val': 1}
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id: 3915395
{'lmfdb_iso': '76050.ef', 'p': 17, 'prec': 20, 'unit': 153915654955472370086036, 'val': 1}
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id: 3915396
{'lmfdb_iso': '76050.ef', 'p': 19, 'prec': 20, 'unit': 1504003261493150263191548, 'val': 1}
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id: 3915398
{'lmfdb_iso': '76050.ef', 'p': 23, 'prec': 20, 'unit': 63722159733582150954967979, 'val': 1}
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id: 3915392
{'lmfdb_iso': '76050.ef', 'p': 29, 'prec': 20, 'unit': 3540874241393657987420133358, 'val': 1}
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id: 3915402
{'lmfdb_iso': '76050.ef', 'p': 31, 'prec': 20, 'unit': 1192546509514735810439411623, 'val': 1}
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id: 3915388
{'lmfdb_iso': '76050.ef', 'p': 37, 'prec': 20, 'unit': 583370700523866458572550324259, 'val': 1}
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id: 3915390
{'lmfdb_iso': '76050.ef', 'p': 41, 'prec': 20, 'unit': 3382468935642842851278307073207, 'val': 1}
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id: 3915391
{'lmfdb_iso': '76050.ef', 'p': 43, 'prec': 20, 'unit': 4594425445124268230051751853254, 'val': 1}
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id: 3915397
{'lmfdb_iso': '76050.ef', 'p': 53, 'prec': 20, 'unit': 484597497444304727279345679920538, 'val': 1}
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id: 3915400
{'lmfdb_iso': '76050.ef', 'p': 59, 'prec': 20, 'unit': 223132953675395450368595978606865, 'val': 1}
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id: 3915401
{'lmfdb_iso': '76050.ef', 'p': 61, 'prec': 20, 'unit': 6802944698769364224269116288376919, 'val': 1}
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id: 3915387
{'lmfdb_iso': '76050.ef', 'p': 67, 'prec': 20, 'unit': 16563089911404016699178800966478998, 'val': 1}
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id: 3915393
{'lmfdb_iso': '76050.ef', 'p': 79, 'prec': 20, 'unit': 12646574403069671461935263634130389, 'val': 2}
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id: 3915386
{'lmfdb_iso': '76050.ef', 'p': 83, 'prec': 20, 'unit': 899724625183571692166740479222440005, 'val': 1}
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id: 3915399
{'lmfdb_iso': '76050.ef', 'p': 89, 'prec': 20, 'unit': 10335052164935440594036056011193531525, 'val': 1}
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id: 3915385
{'lmfdb_iso': '76050.ef', 'p': 97, 'prec': 20, 'unit': 42761638659022626911515815639781697868, 'val': 1}