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ec_curvedata • Show schema
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{'Ciso': '54978bf', 'Clabel': '54978bf1', 'Cnumber': 1, 'abc_quality': 0.965400307655232, 'absD': 102184927673823230544, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 5236, 'ainvs': [1, 0, 1, -2387404, -1501019110], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 54978, 'degree': 2064384, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5909337670437791193221142501', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1], 'jinv': [-12791249261627475241, 868557554027856], 'lmfdb_iso': '54978.u', 'lmfdb_label': '54978.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -48722, 4355268], 'min_quad_twist_disc': -7, 'modell_images': [], 'modm_images': ['5236.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.12203118002613269673626240943', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6179786925161224667694378784', 'prec': 100}, 'szpiro_ratio': 5.110700251927658, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 1, 1, -1, -1, 0, -1, 1, 1, 1, 1, 1, 0, -1, 1, 1, -1, -8, -1], 'aplist': [-1, 1, -1, 0, 1, 1, 1, -8, -1, -1, 10, 4, 0, -9, -4, 7, 9, 8, -8, -3, 6, -6, -6, -6, 2], 'class_deg': 1, 'class_size': 1, 'conductor': 54978, 'isogeny_matrix': [[1]], 'lmfdb_iso': '54978.u', 'trace_hash': 832042098708704644}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0056175057288262198615459191492', 'prec': 110}, 'conductor': 54978, 'gens': [[2125, 53915, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.12203118002613269673626240943', 'prec': 103}], 'lmfdb_label': '54978.u1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.060490922383334358683211746809', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9605552456146366766885389992558422248', 'prec': 130}, 'tamagawa_product': 672, 'torsion_generators': [], 'xcoord_integral_points': [1938, 2125, 6052, 8593, 222037]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 0], '3': [6, 0], '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '54978.u1'}
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ec_torsion_growth • Show schema
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id: 2656297
{'degree': 3, 'field': [14, 0, -1, 1], 'lmfdb_label': '54978.u1', 'torsion': [2]}
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id: 2656298
{'degree': 6, 'field': [5236, 0, 1, 0, -2, 0, 1], 'lmfdb_label': '54978.u1', 'torsion': [2, 2]}
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id: 2656299
{'degree': 8, 'field': [-12024, 11133, -11466, 665, -329, -7, 7, -4, 1], 'lmfdb_label': '54978.u1', 'torsion': [3]}
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id: 2656300
{'degree': 12, 'field': [-299824, -3416, 430141, 283624, 89075, 46068, 13329, 3960, 313, 200, 35, -4, 1], 'lmfdb_label': '54978.u1', 'torsion': [4]}
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ec_localdata • Show schema
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id: 1320608
{'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '54978.u1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1320609
{'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '54978.u1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 1320610
{'conductor': 54978, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '54978.u1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1320611
{'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '54978.u1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
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id: 1320612
{'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54978.u1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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{'adelic_gens': [[2619, 2, 2619, 3], [1, 0, 2, 1], [1, 1, 5235, 0], [1, 2, 0, 1], [3741, 2, 3741, 3], [5235, 2, 5234, 3], [1905, 2, 1905, 3], [309, 2, 309, 3]], 'adelic_image': '5236.2.0.?', 'conductor': 54978, 'lmfdb_label': '54978.u1', 'prime': 0}
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ec_padic • Show schema
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id: 2781377
{'lmfdb_iso': '54978.u', 'p': 5, 'prec': 20, 'unit': 496210471699, 'val': 1}
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id: 2781383
{'lmfdb_iso': '54978.u', 'p': 13, 'prec': 20, 'unit': 13741332986729294923111, 'val': -1}
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id: 2781386
{'lmfdb_iso': '54978.u', 'p': 19, 'prec': 20, 'unit': 78210203730985635387578, 'val': 1}
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id: 2781388
{'lmfdb_iso': '54978.u', 'p': 23, 'prec': 20, 'unit': 39622175754859185981373626, 'val': 1}
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id: 2781382
{'lmfdb_iso': '54978.u', 'p': 29, 'prec': 20, 'unit': 2653561902222977509640015901, 'val': 1}
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id: 2781379
{'lmfdb_iso': '54978.u', 'p': 31, 'prec': 20, 'unit': 324043667153412463473242763, 'val': 2}
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id: 2781392
{'lmfdb_iso': '54978.u', 'p': 37, 'prec': 20, 'unit': 344181192734378788015689572405, 'val': 1}
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id: 2781381
{'lmfdb_iso': '54978.u', 'p': 43, 'prec': 20, 'unit': 2573923557435158555603431245560, 'val': 1}
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id: 2781390
{'lmfdb_iso': '54978.u', 'p': 47, 'prec': 20, 'unit': 43483048161090289145190531025572, 'val': 1}
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id: 2781387
{'lmfdb_iso': '54978.u', 'p': 53, 'prec': 20, 'unit': 338549246396227435321701164773917, 'val': 1}
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id: 2781385
{'lmfdb_iso': '54978.u', 'p': 59, 'prec': 20, 'unit': 2644838846052083137333085680289263, 'val': 1}
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id: 2781391
{'lmfdb_iso': '54978.u', 'p': 61, 'prec': 20, 'unit': 5269661686723381091784778142379237, 'val': 1}
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id: 2781376
{'lmfdb_iso': '54978.u', 'p': 67, 'prec': 20, 'unit': 25833854233925904730883172795075745, 'val': 1}
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id: 2781378
{'lmfdb_iso': '54978.u', 'p': 71, 'prec': 20, 'unit': 63964633572403394839474697255641824, 'val': 1}
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id: 2781380
{'lmfdb_iso': '54978.u', 'p': 73, 'prec': 20, 'unit': 158153570039269696653540628754680506, 'val': 1}
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id: 2781384
{'lmfdb_iso': '54978.u', 'p': 79, 'prec': 20, 'unit': 340218107991936923013222939101398045, 'val': 1}
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id: 2781375
{'lmfdb_iso': '54978.u', 'p': 83, 'prec': 20, 'unit': 2045647540343862374962813811044091876, 'val': 1}
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id: 2781389
{'lmfdb_iso': '54978.u', 'p': 89, 'prec': 20, 'unit': 9612039898969628003869514553414148937, 'val': 1}
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id: 2781374
{'lmfdb_iso': '54978.u', 'p': 97, 'prec': 20, 'unit': 18005149948915138658145191613341357593, 'val': 1}