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ec_curvedata • Show schema
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{'Ciso': '45968p', 'Clabel': '45968p1', 'Cnumber': 1, 'abc_quality': 1.024323072883995, 'absD': 336100364288, 'adelic_genus': 53, 'adelic_index': 1536, 'adelic_level': 14144, 'ainvs': [0, 0, 0, -1859, -13182], 'analytic_rank': 1, 'bad_primes': [2, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 45968, 'degree': 36864, 'elladic_images': ['32.48.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.90583855778942488706931071655', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [35937, 17], 'lmfdb_iso': '45968.k', 'lmfdb_label': '45968.k3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -1, 0], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.o.1', '16.24.0.j.1', '32.48.0.f.2', '34.6.0.a.1', '52.12.0-4.c.1.1', '68.12.0.g.1', '104.24.0.?', '136.48.0.?', '208.48.0.?', '272.192.7.?', '416.96.0.?', '544.384.21.?', '884.24.0.?', '1088.768.53.?', '1768.96.0.?', '3536.384.7.?', '7072.768.21.?', '14144.1536.53.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.5614542424868685764457284837', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0697833015012887903746651257', 'prec': 103}, 'szpiro_ratio': 3.1853519106746973, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 2, 0, 4, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0], 'aplist': [0, 0, 2, 4, 0, 0, 1, -4, -4, 6, 4, 2, 6, -4, 0, 6, -12, -10, 4, -4, 6, -12, -4, -10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 45968, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '45968.k', 'trace_hash': 1362475566954039447}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.16337989992807562158120908227', 'prec': 103}, 'conductor': 45968, 'gens': [[-39, 507, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '2.5614542424868685764457284837', 'prec': 100}], 'lmfdb_label': '45968.k3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.76153101379383695916392744387', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.8025073842701988524476021858430866612', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-39, 0, 1]], 'xcoord_integral_points': [-39]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 5, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [2, 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': '45968.k3'}
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ec_torsion_growth • Show schema
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id: 2244115
{'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '45968.k3', 'torsion': [2, 2]}
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id: 2244116
{'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '45968.k3', 'torsion': [4]}
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id: 2244117
{'degree': 2, 'field': [221, 0, 1], 'lmfdb_label': '45968.k3', 'torsion': [4]}
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id: 2244118
{'degree': 4, 'field': [302, -18, 19, -2, 1], 'lmfdb_label': '45968.k3', 'torsion': [2, 4]}
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id: 2244122
{'degree': 8, 'field': [-85683, 0, 19773, 0, -1014, 0, 0, 0, 1], 'lmfdb_label': '45968.k3', 'torsion': [6]}
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id: 2244119
{'degree': 8, 'field': [-157, 788, -768, -28, -15, 32, -6, -4, 1], 'lmfdb_label': '45968.k3', 'torsion': [2, 4]}
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id: 2244120
{'degree': 8, 'field': [100, 0, -88, 0, 69, 0, -14, 0, 1], 'lmfdb_label': '45968.k3', 'torsion': [8]}
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id: 2244121
{'degree': 8, 'field': [64052, -3456, 12092, -768, 933, -64, 41, -2, 1], 'lmfdb_label': '45968.k3', 'torsion': [2, 8]}
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id: 2244124
{'degree': 16, 'field': [256, 0, 5296, 0, 2369, 0, 11360, 0, 10112, 0, 3350, 0, 504, 0, 36, 0, 1], 'lmfdb_label': '45968.k3', 'torsion': [2, 8]}
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id: 2244123
{'degree': 16, 'field': [47089, 0, -39828, 0, 59154, 0, 924, 0, 3283, 0, -1644, 0, 282, 0, -24, 0, 1], 'lmfdb_label': '45968.k3', 'torsion': [4, 4]}
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id: 2244125
{'degree': 16, 'field': [883119472, 5702492720, -2092299112, -1572448416, 512106224, 123712684, -50346608, -2129544, 1590109, -156324, 32656, 4364, -2152, 84, -7, -2, 1], 'lmfdb_label': '45968.k3', 'torsion': [2, 6]}
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id: 2244126
{'degree': 16, 'field': [944282197, -577527088, 729679286, -327201870, 223002968, -77456108, 36503947, -9965928, 3535756, -752004, 207757, -33256, 7211, -798, 134, -8, 1], 'lmfdb_label': '45968.k3', 'torsion': [12]}
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id: 2244127
{'degree': 16, 'field': [10163241037, 3062106496, -2655376227, -780271270, 308569616, 93902676, -24565781, -5981612, 1741821, -141890, 6037, 12108, -1927, -70, 30, -8, 1], 'lmfdb_label': '45968.k3', 'torsion': [12]}
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ec_localdata • Show schema
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id: 1095624
{'conductor': 45968, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '45968.k3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1095625
{'conductor': 45968, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '45968.k3', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 1095626
{'conductor': 45968, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '45968.k3', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1970385
{'adelic_gens': [[10232, 1105, 13247, 1418], [1, 64, 0, 1], [59, 10, 1662, 2679], [12325, 12948, 1040, 417], [15, 286, 12282, 5987], [1, 0, 64, 1], [6447, 10816, 3562, 753], [14081, 64, 14080, 65], [10879, 0, 0, 14143]], 'adelic_image': '14144.1536.53.?', 'conductor': 45968, 'lmfdb_label': '45968.k3', 'prime': 0}
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id: 199127
{'conductor': 45968, 'elladic_image': '32.48.0.12', 'lmfdb_label': '45968.k3', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 2301836
{'lmfdb_iso': '45968.k', 'p': 5, 'prec': 20, 'unit': 1743832882607, 'val': 1}
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id: 2301837
{'lmfdb_iso': '45968.k', 'p': 7, 'prec': 20, 'unit': 9658430786353136, 'val': 1}
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id: 2301833
{'lmfdb_iso': '45968.k', 'p': 19, 'prec': 20, 'unit': 1760482336081327255269207, 'val': 1}
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id: 2301846
{'lmfdb_iso': '45968.k', 'p': 23, 'prec': 20, 'unit': 67604979992483626721949208, 'val': 1}
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id: 2301841
{'lmfdb_iso': '45968.k', 'p': 29, 'prec': 20, 'unit': 3608611083386803378557168506, 'val': 1}
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id: 2301838
{'lmfdb_iso': '45968.k', 'p': 31, 'prec': 20, 'unit': 9956939402466910179628095630, 'val': 1}
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id: 2301851
{'lmfdb_iso': '45968.k', 'p': 37, 'prec': 20, 'unit': 52691967273601950012610896123, 'val': 1}
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id: 2301839
{'lmfdb_iso': '45968.k', 'p': 41, 'prec': 20, 'unit': 3122211426456707222402961449763, 'val': 1}
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id: 2301840
{'lmfdb_iso': '45968.k', 'p': 43, 'prec': 20, 'unit': 1584882136417395898871940359152, 'val': 1}
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id: 2301844
{'lmfdb_iso': '45968.k', 'p': 53, 'prec': 20, 'unit': 297009313172173617211035244620569, 'val': 1}
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id: 2301849
{'lmfdb_iso': '45968.k', 'p': 59, 'prec': 20, 'unit': 397982328886519744955360322238738, 'val': 1}
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id: 2301850
{'lmfdb_iso': '45968.k', 'p': 61, 'prec': 20, 'unit': 5908874020578462830682026138535310, 'val': 1}
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id: 2301835
{'lmfdb_iso': '45968.k', 'p': 67, 'prec': 20, 'unit': 43302968065428423153463461838884670, 'val': 1}
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id: 2301848
{'lmfdb_iso': '45968.k', 'p': 71, 'prec': 20, 'unit': 24261295046734013028245945623509403, 'val': 1}
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id: 2301845
{'lmfdb_iso': '45968.k', 'p': 73, 'prec': 20, 'unit': 118367024279494591800448835435689618, 'val': 1}
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id: 2301842
{'lmfdb_iso': '45968.k', 'p': 79, 'prec': 20, 'unit': 1054256626585561415462402008313408071, 'val': 1}
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id: 2301843
{'lmfdb_iso': '45968.k', 'p': 83, 'prec': 20, 'unit': 181204846942868400375610703919708917, 'val': 1}
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id: 2301847
{'lmfdb_iso': '45968.k', 'p': 89, 'prec': 20, 'unit': 1641065375756279026143041202322233205, 'val': 1}
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id: 2301834
{'lmfdb_iso': '45968.k', 'p': 97, 'prec': 20, 'unit': 4713891277877646815447825455724757432, 'val': 1}