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ec_curvedata • Show schema
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{'Ciso': '59850br', 'Clabel': '59850br3', 'Cnumber': 3, 'abc_quality': 1.1447961981888821, 'absD': 1016530255766592000000, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 23940, 'ainvs': [1, -1, 0, -2514492, -46545584], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 59850, 'degree': 3981312, 'elladic_images': ['2.3.0.1', '3.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7203786019370095386998569494', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [154357248921765625, 89242711068672], 'lmfdb_iso': '59850.a', 'lmfdb_label': '59850.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -11176, 13046], 'min_quad_twist_disc': -15, 'modell_images': ['2B', '3Cs'], 'modm_images': ['2.3.0.a.1', '3.12.0.a.1', '6.36.0.a.1', '15.24.0-3.a.1.1', '28.6.0.b.1', '30.72.0-6.a.1.1', '84.72.1.?', '114.72.1.?', '420.144.1.?', '570.144.1.?', '1197.36.0.?', '1596.144.5.?', '2394.216.7.?', '4788.432.21.?', '5985.72.0.?', '7980.288.5.?', '11970.432.7.?', '23940.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.4592000239830585718527486470', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3663535013859045057018546643', 'prec': 100}, 'szpiro_ratio': 5.07530855743058, '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, -1, -1, 0, 0, -6, 0, 4, 1, 0, 1, 0, 0, 1, 0], 'aplist': [-1, 0, 0, -1, -6, 4, 0, 1, 6, -6, -4, -2, 6, -8, 12, 6, 12, -10, -14, 12, -2, -10, 12, -18, -8], 'class_deg': 18, 'class_size': 6, 'conductor': 59850, 'isogeny_matrix': [[1, 2, 3, 6, 9, 18], [2, 1, 6, 3, 18, 9], [3, 6, 1, 2, 3, 6], [6, 3, 2, 1, 6, 3], [9, 18, 3, 6, 1, 2], [18, 9, 6, 3, 2, 1]], 'lmfdb_iso': '59850.a', 'trace_hash': 2198452745277755874}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0043361986409192031786810066467', 'prec': 110}, 'conductor': 59850, 'gens': [[-1000, 38804, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.4592000239830585718527486470', 'prec': 100}], 'lmfdb_label': '59850.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13116657257172041289687833909', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8707780609698051846329770741746835621', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-1576, 788, 1]], 'xcoord_integral_points': [-1576, -1000, 6999]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [5, 0], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [2, 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': '59850.a4'}
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ec_torsion_growth • Show schema
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id: 2875104
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 2]}
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id: 2875105
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '59850.a4', 'torsion': [6]}
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id: 2875106
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '59850.a4', 'torsion': [6]}
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id: 2875108
{'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '59850.a4', 'torsion': [3, 6]}
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id: 2875110
{'degree': 4, 'field': [96, -39, 7, -1, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 6]}
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id: 2875107
{'degree': 4, 'field': [149, -70, 29, 0, 1], 'lmfdb_label': '59850.a4', 'torsion': [4]}
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id: 2875109
{'degree': 4, 'field': [169, 0, -31, 0, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 6]}
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id: 2875114
{'degree': 8, 'field': [281, -166, 340, 126, -15, 18, 8, -4, 1], 'lmfdb_label': '59850.a4', 'torsion': [12]}
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id: 2875113
{'degree': 8, 'field': [1296, 0, -252, 0, 13, 0, -7, 0, 1], 'lmfdb_label': '59850.a4', 'torsion': [6, 6]}
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id: 2875115
{'degree': 8, 'field': [3844, 1148, 1350, 266, 137, -14, -8, 0, 1], 'lmfdb_label': '59850.a4', 'torsion': [12]}
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id: 2875111
{'degree': 8, 'field': [51450, 7350, -22785, 1890, 2926, -2, -102, -2, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 4]}
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id: 2875112
{'degree': 8, 'field': [280084, -27832, 34132, 8372, 1269, 160, 37, -2, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 4]}
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id: 2875117
{'degree': 16, 'field': [10084, -54068, 19202, 144466, 251549, 139958, 16008, 8834, 9432, 2086, 578, 434, 144, -14, -18, 0, 1], 'lmfdb_label': '59850.a4', 'torsion': [3, 12]}
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id: 2875118
{'degree': 16, 'field': [45079, 16677792, -9323566, -14118868, 5661626, 1479024, -206050, -161892, -57653, 54960, -1202, -4508, 84, 280, -20, -8, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 12]}
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id: 2875119
{'degree': 16, 'field': [890496, -1203264, 1859040, -1522368, 1336872, -834588, 541218, -274764, 136075, -54236, 20866, -6380, 1852, -392, 76, -8, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 12]}
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id: 2875121
{'degree': 16, 'field': [2042041, -1486160, 4164599, -8403252, 9128110, -6109042, 3610893, -1462970, 527130, -120620, 26385, -2032, 286, 78, 11, -2, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 12]}
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id: 2875120
{'degree': 16, 'field': [38277124, -43191316, 32723686, -12190262, 5294225, -2549064, 900646, -303240, 120378, -30254, 11070, -1848, 822, -56, 44, 0, 1], 'lmfdb_label': '59850.a4', 'torsion': [2, 12]}
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id: 2875116
{'degree': 16, 'field': [11638722916, -997197216, 994999904, 10627460, -21142987, 19663338, -7594306, 736158, 26890, -167676, 61726, -16838, 4050, -602, 106, -8, 1], 'lmfdb_label': '59850.a4', 'torsion': [8]}
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id: 2875123
{'degree': 18, 'field': [10077696, 0, 0, 126531072, 0, 0, 470908872, 0, 0, 1755189, 0, 0, -27888, 0, 0, -81, 0, 0, 1], 'lmfdb_label': '59850.a4', 'torsion': [18]}
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id: 2875122
{'degree': 18, 'field': [359403152669, -449787567423, 22469563737, 164522092098, -38964949452, -26017480386, 7942886880, 2361987690, -776412549, -136687175, 43076565, 5197410, -1403694, -125412, 26028, 1692, -249, -9, 1], 'lmfdb_label': '59850.a4', 'torsion': [18]}
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ec_localdata • Show schema
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id: 1441428
{'conductor': 59850, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '59850.a4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1441429
{'conductor': 59850, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '59850.a4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 1441430
{'conductor': 59850, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '59850.a4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 1441431
{'conductor': 59850, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '59850.a4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1441432
{'conductor': 59850, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '59850.a4', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 2060999
{'adelic_gens': [[14363, 0, 0, 23939], [19, 24, 1440, 1819], [10366, 19155, 2505, 14296], [1, 0, 36, 1], [23905, 36, 23904, 37], [1, 36, 0, 1], [1, 6, 6, 37], [15061, 14400, 14790, 10861], [9574, 14355, 19305, 7604], [10801, 5190, 20610, 12511]], 'adelic_image': '23940.864.21.?', 'conductor': 59850, 'lmfdb_label': '59850.a4', 'prime': 0}
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id: 252984
{'conductor': 59850, 'elladic_image': '2.3.0.1', 'lmfdb_label': '59850.a4', 'modell_image': '2B', 'prime': 2}
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id: 252985
{'conductor': 59850, 'elladic_image': '3.12.0.1', 'lmfdb_label': '59850.a4', 'modell_image': '3Cs', 'prime': 3}
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ec_padic • Show schema
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id: 3040452
{'lmfdb_iso': '59850.a', 'p': 11, 'prec': 20, 'unit': 21064117184457771045, 'val': 1}
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id: 3040458
{'lmfdb_iso': '59850.a', 'p': 13, 'prec': 20, 'unit': 1408856419939051576989, 'val': 1}
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id: 3040464
{'lmfdb_iso': '59850.a', 'p': 23, 'prec': 20, 'unit': 46290429823104764810289562, 'val': 1}
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id: 3040457
{'lmfdb_iso': '59850.a', 'p': 29, 'prec': 20, 'unit': 3949065396658320698148181413, 'val': 1}
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id: 3040468
{'lmfdb_iso': '59850.a', 'p': 31, 'prec': 20, 'unit': 11905094378732138485059616470, 'val': 1}
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id: 3040453
{'lmfdb_iso': '59850.a', 'p': 37, 'prec': 20, 'unit': 247603059627212160104323698262, 'val': 1}
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id: 3040455
{'lmfdb_iso': '59850.a', 'p': 41, 'prec': 20, 'unit': 2219832172634342549521756399437, 'val': 1}
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id: 3040456
{'lmfdb_iso': '59850.a', 'p': 43, 'prec': 20, 'unit': 6651990788544605555658059441991, 'val': 1}
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id: 3040466
{'lmfdb_iso': '59850.a', 'p': 47, 'prec': 20, 'unit': 11695419120802060938485744835153, 'val': 1}
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id: 3040462
{'lmfdb_iso': '59850.a', 'p': 53, 'prec': 20, 'unit': 355007058504711016526303476640175, 'val': 1}
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id: 3040460
{'lmfdb_iso': '59850.a', 'p': 59, 'prec': 20, 'unit': 408099616531709889193135655891914, 'val': 1}
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id: 3040467
{'lmfdb_iso': '59850.a', 'p': 61, 'prec': 20, 'unit': 2184623250850394945620083457695121, 'val': 1}
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id: 3040461
{'lmfdb_iso': '59850.a', 'p': 67, 'prec': 20, 'unit': 47614426738567537375023558318636152, 'val': 1}
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id: 3040454
{'lmfdb_iso': '59850.a', 'p': 71, 'prec': 20, 'unit': 38989817721650285769753559533470416, 'val': 1}
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id: 3040463
{'lmfdb_iso': '59850.a', 'p': 73, 'prec': 20, 'unit': 161418576739812422676316484300974083, 'val': 1}
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id: 3040459
{'lmfdb_iso': '59850.a', 'p': 79, 'prec': 20, 'unit': 359529672957229649690233584400535978, 'val': 1}
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id: 3040451
{'lmfdb_iso': '59850.a', 'p': 83, 'prec': 20, 'unit': 691773097907079117312254214191273216, 'val': 1}
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id: 3040465
{'lmfdb_iso': '59850.a', 'p': 89, 'prec': 20, 'unit': 7201797783839342239024906954310401463, 'val': 1}
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id: 3040450
{'lmfdb_iso': '59850.a', 'p': 97, 'prec': 20, 'unit': 3992516765474318264785635865581944605, 'val': 1}