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ec_curvedata • Show schema
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{'Ciso': '25872q', 'Clabel': '25872q1', 'Cnumber': 1, 'abc_quality': 0.9881573626459625, 'absD': 250024176154368, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 616, 'ainvs': [0, 1, 0, 1356, -760068], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 25872, 'degree': 98304, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4417298846702513905254136949', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 43, 'isogeny_degrees': [1, 2, 4], 'jinv': [9148592, 8301447], 'lmfdb_iso': '25872.br', 'lmfdb_label': '25872.br4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 28, -2208], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '14.6.0.b.1', '28.24.0-28.g.1.1', '88.24.0.?', '616.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3745024383173776668622491233', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0066766897692978650279159088730', 'prec': 110}, 'szpiro_ratio': 3.9963580444231654, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, -2, 0, 0, 0, 1, 0, -1, 0, -6, 0, -2, 0, -6, 0, 0, 0], 'aplist': [0, 1, -2, 0, -1, -6, -6, 0, 8, -2, 4, -2, 2, 12, 12, 6, 4, -6, -4, 0, 2, -8, 0, 6, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 25872, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '25872.br', 'trace_hash': 1885368168621127330}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.055940885082287693593905145443', 'prec': 107}, 'conductor': 25872, 'gens': [[207, 2904, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3745024383173776668622491233', 'prec': 100}], 'lmfdb_label': '25872.br4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25842963036701634860571495813', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9091342995195115814726813051949445492', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[86, 0, 1]], 'xcoord_integral_points': [86, 207, 282]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 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': '25872.br4'}
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ec_torsion_growth • Show schema
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id: 1302009
{'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '25872.br4', 'torsion': [4]}
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id: 1302010
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '25872.br4', 'torsion': [4]}
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id: 1302008
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '25872.br4', 'torsion': [2, 2]}
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id: 1302011
{'degree': 4, 'field': [2, -4, 3, -1, 1], 'lmfdb_label': '25872.br4', 'torsion': [2, 4]}
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id: 1302012
{'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '25872.br4', 'torsion': [2, 4]}
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id: 1302016
{'degree': 8, 'field': [-964467, 0, 167832, 0, 3402, 0, 0, 0, 1], 'lmfdb_label': '25872.br4', 'torsion': [6]}
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id: 1302013
{'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '25872.br4', 'torsion': [4, 4]}
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id: 1302014
{'degree': 8, 'field': [196, 0, -476, 0, 53, 0, 10, 0, 1], 'lmfdb_label': '25872.br4', 'torsion': [8]}
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id: 1302015
{'degree': 8, 'field': [16641, 0, -2222, 0, -137, 0, 22, 0, 1], 'lmfdb_label': '25872.br4', 'torsion': [8]}
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id: 1302017
{'degree': 16, 'field': [207, 1098, 5154, 12222, 22897, 21154, 14980, -960, 2592, -1138, 714, -434, 147, -42, 16, -4, 1], 'lmfdb_label': '25872.br4', 'torsion': [2, 8]}
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id: 1302021
{'degree': 16, 'field': [9216, 0, -460800, 0, 1149696, 0, -11435008, 0, 903680, 0, -21856, 0, 928, 0, -56, 0, 1], 'lmfdb_label': '25872.br4', 'torsion': [12]}
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id: 1302019
{'degree': 16, 'field': [178084, -40512, 4608, 72072, -33544, -11728, 18120, -11204, 981, 2108, -1240, 332, 66, -84, 32, -8, 1], 'lmfdb_label': '25872.br4', 'torsion': [2, 8]}
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id: 1302018
{'degree': 16, 'field': [567009, 743964, 488072, 144828, 88302, 976, -56232, 59476, -4877, -14008, 9768, -2740, 386, -20, 32, -8, 1], 'lmfdb_label': '25872.br4', 'torsion': [2, 8]}
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id: 1302020
{'degree': 16, 'field': [4624928, -9099104, 15814576, -15335872, 12573800, -6286728, 2754700, -549880, 116357, 17456, -6624, 1376, 74, -168, 44, -8, 1], 'lmfdb_label': '25872.br4', 'torsion': [2, 6]}
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id: 1302022
{'degree': 16, 'field': [4978149136, -2840302336, 810272768, -982695840, 461928992, 26018608, 6961696, -3480096, 1128184, -83616, -26936, 9968, -1540, -84, 32, -8, 1], 'lmfdb_label': '25872.br4', 'torsion': [12]}
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ec_localdata • Show schema
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id: 595923
{'conductor': 25872, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '25872.br4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 595924
{'conductor': 25872, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '25872.br4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 595925
{'conductor': 25872, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '25872.br4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 595926
{'conductor': 25872, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '25872.br4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1836849
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [256, 613, 83, 614], [57, 8, 228, 33], [609, 8, 608, 9], [7, 6, 610, 611], [547, 542, 82, 387], [223, 228, 226, 537]], 'adelic_image': '616.48.0.?', 'conductor': 25872, 'lmfdb_label': '25872.br4', 'prime': 0}
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id: 117861
{'conductor': 25872, 'elladic_image': '4.12.0.8', 'lmfdb_label': '25872.br4', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 1234207
{'lmfdb_iso': '25872.br', 'p': 5, 'prec': 20, 'unit': 17469432631424, 'val': 1}
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id: 1234212
{'lmfdb_iso': '25872.br', 'p': 13, 'prec': 20, 'unit': 340079050354446193078, 'val': 1}
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id: 1234214
{'lmfdb_iso': '25872.br', 'p': 17, 'prec': 20, 'unit': 157417926546025289164224, 'val': 1}
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id: 1234218
{'lmfdb_iso': '25872.br', 'p': 23, 'prec': 20, 'unit': 18204626807597950143158402, 'val': 1}
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id: 1234211
{'lmfdb_iso': '25872.br', 'p': 29, 'prec': 20, 'unit': 2498970180707438645392403468, 'val': 1}
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id: 1234208
{'lmfdb_iso': '25872.br', 'p': 31, 'prec': 20, 'unit': 3506171649392706506134766604, 'val': 1}
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id: 1234222
{'lmfdb_iso': '25872.br', 'p': 37, 'prec': 20, 'unit': 515523032539475737418107832377, 'val': 1}
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id: 1234209
{'lmfdb_iso': '25872.br', 'p': 41, 'prec': 20, 'unit': 3666451643133743190941404811828, 'val': 1}
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id: 1234210
{'lmfdb_iso': '25872.br', 'p': 43, 'prec': 20, 'unit': 10196664451109424528686504656087, 'val': 1}
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id: 1234220
{'lmfdb_iso': '25872.br', 'p': 47, 'prec': 20, 'unit': 57413987834877809141695065615519, 'val': 1}
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id: 1234215
{'lmfdb_iso': '25872.br', 'p': 53, 'prec': 20, 'unit': 57723818969127229337949587854, 'val': 1}
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id: 1234216
{'lmfdb_iso': '25872.br', 'p': 59, 'prec': 20, 'unit': 1634802909034292597417209668808740, 'val': 1}
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id: 1234221
{'lmfdb_iso': '25872.br', 'p': 61, 'prec': 20, 'unit': 8243299336400634945597989030709693, 'val': 1}
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id: 1234206
{'lmfdb_iso': '25872.br', 'p': 67, 'prec': 20, 'unit': 18141235196212058863760122630809825, 'val': 1}
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id: 1234217
{'lmfdb_iso': '25872.br', 'p': 73, 'prec': 20, 'unit': 7275554838139070000632534571806857, 'val': 1}
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id: 1234213
{'lmfdb_iso': '25872.br', 'p': 79, 'prec': 20, 'unit': 661478273390084324828723959891936986, 'val': 1}
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id: 1234219
{'lmfdb_iso': '25872.br', 'p': 89, 'prec': 20, 'unit': 7976573421130674567213038906751183060, 'val': 1}
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id: 1234205
{'lmfdb_iso': '25872.br', 'p': 97, 'prec': 20, 'unit': 22107168078523607164773709141352622265, 'val': 1}