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ec_curvedata • Show schema
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{'Ciso': '28322bb', 'Clabel': '28322bb2', 'Cnumber': 2, 'abc_quality': 0.9583841923148042, 'absD': 252221288974089959552, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 136, 'ainvs': [1, 0, 0, -9912995, -11989610879], 'analytic_rank': 1, 'bad_primes': [2, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 28322, 'degree': 3096576, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7950072136441674939945666650', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2], 'jinv': [37936442980801, 88817792], 'lmfdb_iso': '28322.q', 'lmfdb_label': '28322.q1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -700, 7056], 'min_quad_twist_disc': -119, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '68.6.0.c.1', '136.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9048015576142337663123660369', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.40544546708840280131712298434', 'prec': 103}, 'szpiro_ratio': 5.847172911869318, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, -2, 1, -4, -2, 0, 1, 1, -4, 6, -2, 2, 0, 8, 1, 0, 1, 0, -4], 'aplist': [1, -2, -4, 0, 6, 2, 0, 0, 4, -8, 0, -4, -2, -8, 8, -6, 4, -8, -16, -4, 10, 12, -12, -10, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 28322, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '28322.q', 'trace_hash': 1789539640027694332}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0037349739787528387619665603974', 'prec': 110}, 'conductor': 28322, 'gens': [[-1812, 5819, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9048015576142337663123660369', 'prec': 100}], 'lmfdb_label': '28322.q1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.085096055636442646347426210174', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.5385507810474565847589453389879166299', 'prec': 130}, 'tamagawa_product': 112, 'torsion_generators': [[-7537, 7537, 2]], 'xcoord_integral_points': [-1812, 3666, 8320]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [8, 1], '3': [1, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '28322.q1'}
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ec_torsion_growth • Show schema
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id: 1420652
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '28322.q1', 'torsion': [2, 2]}
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id: 1420653
{'degree': 4, 'field': [98, 0, 35, 0, 1], 'lmfdb_label': '28322.q1', 'torsion': [4]}
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id: 1420655
{'degree': 8, 'field': [2809, 0, 426, 0, 394, 0, 26, 0, 1], 'lmfdb_label': '28322.q1', 'torsion': [2, 4]}
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id: 1420656
{'degree': 8, 'field': [8232, -4116, 3234, -3479, 644, -161, -17, -4, 1], 'lmfdb_label': '28322.q1', 'torsion': [6]}
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id: 1420654
{'degree': 8, 'field': [14686, 16800, -4072, -72, -47, -12, -14, -4, 1], 'lmfdb_label': '28322.q1', 'torsion': [2, 4]}
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id: 1420657
{'degree': 16, 'field': [440896, 0, 2051284, 0, 1695553, 0, 576514, 0, 89163, 0, 4992, 0, 27, 0, 18, 0, 1], 'lmfdb_label': '28322.q1', 'torsion': [8]}
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id: 1420658
{'degree': 16, 'field': [18203336, -445655408, 245340796, -96410624, -7866042, -14353508, 9672809, -3655348, 1635252, -248194, 29377, -7652, 3093, -74, -34, -8, 1], 'lmfdb_label': '28322.q1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 657010
{'conductor': 28322, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '28322.q1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
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id: 657011
{'conductor': 28322, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '28322.q1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 657012
{'conductor': 28322, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '28322.q1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1853320
{'adelic_gens': [[133, 4, 132, 5], [2, 1, 67, 0], [1, 4, 0, 1], [1, 0, 4, 1], [3, 4, 8, 11], [121, 18, 16, 119], [1, 2, 2, 5], [105, 4, 74, 9]], 'adelic_image': '136.12.0.?', 'conductor': 28322, 'lmfdb_label': '28322.q1', 'prime': 0}
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id: 128164
{'conductor': 28322, 'elladic_image': '8.6.0.6', 'lmfdb_label': '28322.q1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 1363031
{'lmfdb_iso': '28322.q', 'p': 5, 'prec': 20, 'unit': 88448163044233, 'val': -1}
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id: 1363015
{'lmfdb_iso': '28322.q', 'p': 11, 'prec': 20, 'unit': 26554286478032175850, 'val': 1}
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id: 1363021
{'lmfdb_iso': '28322.q', 'p': 13, 'prec': 20, 'unit': 525412777619642918442, 'val': 1}
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id: 1363027
{'lmfdb_iso': '28322.q', 'p': 23, 'prec': 20, 'unit': 20044221035462814107798034, 'val': 1}
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id: 1363020
{'lmfdb_iso': '28322.q', 'p': 29, 'prec': 20, 'unit': 5117940747196480896463518611, 'val': 1}
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id: 1363016
{'lmfdb_iso': '28322.q', 'p': 37, 'prec': 20, 'unit': 240672014204486528418395353088, 'val': 1}
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id: 1363018
{'lmfdb_iso': '28322.q', 'p': 41, 'prec': 20, 'unit': 1162630784603954537877242516521, 'val': 1}
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id: 1363019
{'lmfdb_iso': '28322.q', 'p': 43, 'prec': 20, 'unit': 1275982408622149162894395140957, 'val': 1}
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id: 1363029
{'lmfdb_iso': '28322.q', 'p': 47, 'prec': 20, 'unit': 1890127917470097439437669981757, 'val': 1}
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id: 1363025
{'lmfdb_iso': '28322.q', 'p': 53, 'prec': 20, 'unit': 452067833037402652368351161791082, 'val': 1}
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id: 1363023
{'lmfdb_iso': '28322.q', 'p': 59, 'prec': 20, 'unit': 1726986632494011546522256106291716, 'val': 1}
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id: 1363030
{'lmfdb_iso': '28322.q', 'p': 61, 'prec': 20, 'unit': 7997416070294260258151792531517697, 'val': 1}
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id: 1363024
{'lmfdb_iso': '28322.q', 'p': 67, 'prec': 20, 'unit': 5527875216976008700650516832064308, 'val': 1}
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id: 1363017
{'lmfdb_iso': '28322.q', 'p': 71, 'prec': 20, 'unit': 14513780828185401560663383325247989, 'val': 1}
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id: 1363026
{'lmfdb_iso': '28322.q', 'p': 73, 'prec': 20, 'unit': 226992674835401878911715137237481428, 'val': 1}
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id: 1363022
{'lmfdb_iso': '28322.q', 'p': 79, 'prec': 20, 'unit': 341899856234099611709913178916241593, 'val': 1}
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id: 1363014
{'lmfdb_iso': '28322.q', 'p': 83, 'prec': 20, 'unit': 505961533334499709952371604429748906, 'val': 1}
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id: 1363028
{'lmfdb_iso': '28322.q', 'p': 89, 'prec': 20, 'unit': 2202290296017334524212199474968438635, 'val': 1}
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id: 1363013
{'lmfdb_iso': '28322.q', 'p': 97, 'prec': 20, 'unit': 12314705716032499077940930517837425299, 'val': 1}