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ec_curvedata • Show schema
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{'Ciso': '342c', 'Clabel': '342c1', 'Cnumber': 1, 'abc_quality': 1.047658380732593, 'absD': 23934528, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 456, 'ainvs': [1, -1, 0, -72, 0], 'analytic_rank': 1, 'bad_primes': [2, 3, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 342, 'degree': 96, 'elladic_images': ['8.6.0.4', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.10550204595010275112532756930', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [57066625, 32832], 'lmfdb_iso': '342.c', 'lmfdb_label': '342.c3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -8, 0], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '6.24.0-6.a.1.2', '8.6.0.d.1', '24.48.0-24.bx.1.11', '114.48.0.?', '456.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.35495045195116794406035805257', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.44380409838395209457229504916', 'prec': 107}, 'szpiro_ratio': 4.190607859747218, '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, -4, -1, 0, 0, 0, 0, -4, 4, 0, 1, -6, 0, 1, 0], 'aplist': [-1, 0, 0, -4, 0, -4, -6, 1, 6, -6, 2, -4, -6, -4, -6, -6, 12, 14, 8, 0, 14, -10, 12, 6, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 342, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '342.c', 'trace_hash': 401333918892878}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.80977075337338488563943233140', 'prec': 103}, 'conductor': 342, 'gens': [[-3, 15, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.35495045195116794406035805257', 'prec': 103}], 'lmfdb_label': '342.c3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.7816724979966209210767679034', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2648109167857339186411249913487300188', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [-8, -3, 0, 9, 24, 289]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 0], '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [1, 3, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '342.c3'}
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ec_torsion_growth • Show schema
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id: 14828
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '342.c3', 'torsion': [2, 2]}
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id: 14829
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '342.c3', 'torsion': [6]}
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id: 14830
{'degree': 3, 'field': [-12, -6, -1, 1], 'lmfdb_label': '342.c3', 'torsion': [6]}
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id: 14831
{'degree': 4, 'field': [3, 2, -1, -2, 1], 'lmfdb_label': '342.c3', 'torsion': [4]}
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id: 14832
{'degree': 4, 'field': [25, -5, -4, -1, 1], 'lmfdb_label': '342.c3', 'torsion': [2, 6]}
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id: 14834
{'degree': 6, 'field': [-8, 1, -5, 7, -1, -3, 1], 'lmfdb_label': '342.c3', 'torsion': [2, 6]}
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id: 14833
{'degree': 6, 'field': [12, 6, -5, -3, 4, -3, 1], 'lmfdb_label': '342.c3', 'torsion': [3, 6]}
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id: 14837
{'degree': 8, 'field': [9, 6, 7, 10, 2, -2, 5, -2, 1], 'lmfdb_label': '342.c3', 'torsion': [12]}
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id: 14836
{'degree': 8, 'field': [36, 0, 444, 0, 13, 0, -2, 0, 1], 'lmfdb_label': '342.c3', 'torsion': [2, 4]}
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id: 14835
{'degree': 8, 'field': [82, -394, -145, 260, 82, -26, -10, -2, 1], 'lmfdb_label': '342.c3', 'torsion': [2, 4]}
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id: 14838
{'degree': 12, 'field': [64, -8, -39, 107, 10, -9, 31, -36, 27, -11, 10, -3, 1], 'lmfdb_label': '342.c3', 'torsion': [6, 6]}
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id: 14839
{'degree': 12, 'field': [64, 64, 336, 304, 20, -80, 138, 40, 5, -38, 21, -2, 1], 'lmfdb_label': '342.c3', 'torsion': [12]}
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id: 14842
{'degree': 16, 'field': [121, -550, 1411, -3058, 4973, -4000, 1542, 548, -634, 52, 270, -128, -19, 34, -5, -2, 1], 'lmfdb_label': '342.c3', 'torsion': [2, 12]}
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id: 14841
{'degree': 16, 'field': [2304, 3456, 1440, -432, -780, -432, 1218, 936, -299, -234, 202, -36, 21, 12, 10, -6, 1], 'lmfdb_label': '342.c3', 'torsion': [2, 12]}
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id: 14840
{'degree': 16, 'field': [140992, 98048, -92224, 122880, 76304, -72640, 104944, -41280, 32380, -8784, 5544, -896, 460, -56, 24, 0, 1], 'lmfdb_label': '342.c3', 'torsion': [8]}
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id: 14843
{'degree': 18, 'field': [256, 384, 3456, -4384, 29856, -7368, 27332, 11232, 24576, 2960, 2094, -3024, 203, 327, 48, -25, 0, -3, 1], 'lmfdb_label': '342.c3', 'torsion': [18]}
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ec_localdata • Show schema
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id: 3337
{'conductor': 342, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '342.c3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 3338
{'conductor': 342, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '342.c3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 3339
{'conductor': 342, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '342.c3', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1667232
{'adelic_gens': [[11, 2, 406, 447], [70, 445, 315, 20], [1, 0, 12, 1], [1, 6, 6, 37], [1, 12, 0, 1], [229, 12, 6, 73], [445, 12, 444, 13], [327, 250, 230, 149], [58, 3, 117, 448]], 'adelic_image': '456.96.1.?', 'conductor': 342, 'lmfdb_label': '342.c3', 'prime': 0}
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id: 1451
{'conductor': 342, 'elladic_image': '8.6.0.4', 'lmfdb_label': '342.c3', 'modell_image': '2B', 'prime': 2}
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id: 1452
{'conductor': 342, 'elladic_image': '3.8.0.2', 'lmfdb_label': '342.c3', 'modell_image': '3B.1.2', 'prime': 3}
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ec_padic • Show schema
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id: 4047
{'lmfdb_iso': '342.c', 'p': 7, 'prec': 20, 'unit': 6769145661301271, 'val': 1}
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id: 4051
{'lmfdb_iso': '342.c', 'p': 13, 'prec': 20, 'unit': 81279469606464671953, 'val': 2}
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id: 4053
{'lmfdb_iso': '342.c', 'p': 17, 'prec': 20, 'unit': 112322830337441201154122, 'val': 1}
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id: 4058
{'lmfdb_iso': '342.c', 'p': 23, 'prec': 20, 'unit': 40425583267658300079814505, 'val': 1}
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id: 4050
{'lmfdb_iso': '342.c', 'p': 29, 'prec': 20, 'unit': 5684019480916885898493796690, 'val': 1}
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id: 4062
{'lmfdb_iso': '342.c', 'p': 31, 'prec': 20, 'unit': 13196649416448469734864662822, 'val': 1}
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id: 4046
{'lmfdb_iso': '342.c', 'p': 37, 'prec': 20, 'unit': 319396460299524070638461976657, 'val': 1}
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id: 4048
{'lmfdb_iso': '342.c', 'p': 41, 'prec': 20, 'unit': 1489938833900276201418236882170, 'val': 1}
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id: 4049
{'lmfdb_iso': '342.c', 'p': 43, 'prec': 20, 'unit': 4430919872315904136962118128189, 'val': 1}
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id: 4060
{'lmfdb_iso': '342.c', 'p': 47, 'prec': 20, 'unit': 28465833444403876132935649593715, 'val': 1}
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id: 4055
{'lmfdb_iso': '342.c', 'p': 53, 'prec': 20, 'unit': 252179874704376174060534604384466, 'val': 1}
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id: 4056
{'lmfdb_iso': '342.c', 'p': 59, 'prec': 20, 'unit': 2682840146508738519094474896984947, 'val': 1}
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id: 4061
{'lmfdb_iso': '342.c', 'p': 61, 'prec': 20, 'unit': 2050353525541648278046033250874478, 'val': 1}
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id: 4045
{'lmfdb_iso': '342.c', 'p': 67, 'prec': 20, 'unit': 22745107747337304063725035563693810, 'val': 1}
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id: 4057
{'lmfdb_iso': '342.c', 'p': 73, 'prec': 20, 'unit': 219720546464974836020793773362724984, 'val': 1}
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id: 4052
{'lmfdb_iso': '342.c', 'p': 79, 'prec': 20, 'unit': 486295208250985496881221892555507316, 'val': 1}
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id: 4054
{'lmfdb_iso': '342.c', 'p': 83, 'prec': 20, 'unit': 1828916768818381614051949538690178748, 'val': 1}
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id: 4059
{'lmfdb_iso': '342.c', 'p': 89, 'prec': 20, 'unit': 4302378727237896135404155168905475491, 'val': 1}
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id: 4044
{'lmfdb_iso': '342.c', 'p': 97, 'prec': 20, 'unit': 8175711886640674396039104054375794935, 'val': 1}