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ec_curvedata • Show schema
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{'Ciso': '1045b', 'Clabel': '1045b4', 'Cnumber': 4, 'abc_quality': 1.0266820965922903, 'absD': 15323275604248046875, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1672, 'ainvs': [1, -1, 0, -948119, -401927292], 'analytic_rank': 1, 'bad_primes': [5, 11, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1045, 'degree': 17664, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4089712693847815425058418295', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [-94256762600623910012361, 15323275604248046875], 'lmfdb_iso': '1045.b', 'lmfdb_label': '1045.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -948119, -401927292], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '38.6.0.b.1', '76.24.0.?', '88.24.0.?', '1672.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6638179689958272347419915734', 'prec': 100}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4089712693847815425058418295', 'prec': 100}, 'szpiro_ratio': 7.645228716961291, '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, 1, 0, 0, -3, -3, 1, -1, 0, 2, 0, 0, -1, -6, -3, 1, -1], 'aplist': [1, 0, 1, 0, -1, 2, -6, 1, -8, -6, 4, -2, -10, 4, 0, -2, -8, 14, 8, -4, 2, -16, -4, 10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 1045, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1045.b', 'trace_hash': 89484167820100000}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0080834013265549262578432891904', 'prec': 110}, 'conductor': 1045, 'gens': [[1292, 22344, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6638179689958272347419915734', 'prec': 100}], 'lmfdb_label': '1045.b4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.075822212874574098349463719319', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0277046455138353542434232563698642628', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[4563, -4563, 2]], 'xcoord_integral_points': [1292, 20672]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 1], '3': [3, 3, 0], '5': [2, 0], '7': [3, 1, 0], '11': [1, 0], '13': [3, 0], '17': [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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1045.b4'}
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ec_torsion_growth • Show schema
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id: 50916
{'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [4]}
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id: 50917
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [4]}
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id: 50915
{'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '1045.b4', 'torsion': [2, 2]}
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id: 50918
{'degree': 4, 'field': [19, 0, 0, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [2, 4]}
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id: 50919
{'degree': 4, 'field': [25, 0, -9, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [2, 4]}
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id: 50923
{'degree': 8, 'field': [-3, 0, 3, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [6]}
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id: 50920
{'degree': 8, 'field': [25, -10, 2, 14, -1, -10, 8, -4, 1], 'lmfdb_label': '1045.b4', 'torsion': [4, 4]}
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id: 50922
{'degree': 8, 'field': [361, 0, 0, 0, 138, 0, 0, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [8]}
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id: 50921
{'degree': 8, 'field': [130321, 0, 0, 0, -2622, 0, 0, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [8]}
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id: 50929
{'degree': 16, 'field': [25, 0, 50, 0, 25, 0, 824, 0, 382, 0, 74, 0, 16, 0, 8, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [12]}
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id: 50924
{'degree': 16, 'field': [2025, 0, 25632, 0, 103046, 0, 24692, 0, 3739, 0, 780, 0, 194, 0, 20, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [2, 8]}
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id: 50925
{'degree': 16, 'field': [160000, 0, 0, 0, -19296, 0, 0, 0, 2393, 0, 0, 0, 27, 0, 0, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [2, 8]}
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id: 50927
{'degree': 16, 'field': [298615, -817030, 1390940, -1362714, 1266743, -844388, 539998, -267792, 129772, -50118, 18850, -5584, 1598, -336, 68, -8, 1], 'lmfdb_label': '1045.b4', 'torsion': [2, 6]}
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id: 50926
{'degree': 16, 'field': [1885902500, -51143000, 87760300, -66729080, 17212354, 19068136, -5825858, -466988, 133533, -13112, 4906, -1724, 712, -224, 52, -8, 1], 'lmfdb_label': '1045.b4', 'torsion': [2, 8]}
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id: 50928
{'degree': 16, 'field': [16437547681, 0, -7202358518, 0, 1343221081, 0, -141002456, 0, 9197626, 0, -384554, 0, 10096, 0, -152, 0, 1], 'lmfdb_label': '1045.b4', 'torsion': [12]}
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ec_localdata • Show schema
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id: 14681
{'conductor': 1045, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '1045.b4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
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id: 14682
{'conductor': 1045, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1045.b4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 14683
{'conductor': 1045, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '1045.b4', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 1671143
{'adelic_gens': [[761, 8, 1372, 33], [624, 3, 181, 2], [1665, 8, 1664, 9], [1, 0, 8, 1], [635, 628, 674, 1469], [7, 6, 1666, 1667], [1467, 1466, 1058, 219], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1672.48.0.?', 'conductor': 1045, 'lmfdb_label': '1045.b4', 'prime': 0}
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id: 4918
{'conductor': 1045, 'elladic_image': '4.12.0.8', 'lmfdb_label': '1045.b4', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 23994
{'lmfdb_iso': '1045.b', 'p': 13, 'prec': 20, 'unit': 48387134605679768859, 'val': 2}
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id: 23996
{'lmfdb_iso': '1045.b', 'p': 17, 'prec': 20, 'unit': 191137214908475878334340, 'val': 1}
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id: 24000
{'lmfdb_iso': '1045.b', 'p': 23, 'prec': 20, 'unit': 52267404802528728270645215, 'val': 1}
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id: 23993
{'lmfdb_iso': '1045.b', 'p': 29, 'prec': 20, 'unit': 345046209706737764912339412, 'val': 1}
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id: 24004
{'lmfdb_iso': '1045.b', 'p': 31, 'prec': 20, 'unit': 3004674695648024654684704016, 'val': 1}
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id: 23989
{'lmfdb_iso': '1045.b', 'p': 37, 'prec': 20, 'unit': 320574506802793872928771388581, 'val': 1}
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id: 23991
{'lmfdb_iso': '1045.b', 'p': 41, 'prec': 20, 'unit': 4066735298071223100663364986338, 'val': 1}
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id: 23992
{'lmfdb_iso': '1045.b', 'p': 43, 'prec': 20, 'unit': 5125273204847364618594856219046, 'val': 1}
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id: 23998
{'lmfdb_iso': '1045.b', 'p': 53, 'prec': 20, 'unit': 377670065232759768866330635460617, 'val': 1}
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id: 24002
{'lmfdb_iso': '1045.b', 'p': 59, 'prec': 20, 'unit': 1000491486374762276172043146605379, 'val': 1}
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id: 24003
{'lmfdb_iso': '1045.b', 'p': 61, 'prec': 20, 'unit': 5754969843246982122878775838516038, 'val': 1}
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id: 23988
{'lmfdb_iso': '1045.b', 'p': 67, 'prec': 20, 'unit': 28301498713088840152661408571871441, 'val': 1}
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id: 23990
{'lmfdb_iso': '1045.b', 'p': 71, 'prec': 20, 'unit': 60039084190142991816179459684766854, 'val': 1}
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id: 23999
{'lmfdb_iso': '1045.b', 'p': 73, 'prec': 20, 'unit': 42145099187000600724663795378224926, 'val': 1}
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id: 23995
{'lmfdb_iso': '1045.b', 'p': 79, 'prec': 20, 'unit': 906478283758850273845027919743210644, 'val': 1}
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id: 23997
{'lmfdb_iso': '1045.b', 'p': 83, 'prec': 20, 'unit': 2526386986941259054610109443020715574, 'val': 1}
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id: 24001
{'lmfdb_iso': '1045.b', 'p': 89, 'prec': 20, 'unit': 2614586800384778664805849348530802313, 'val': 1}
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id: 23987
{'lmfdb_iso': '1045.b', 'p': 97, 'prec': 20, 'unit': 8905861191286106034753378051279609720, 'val': 1}