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ec_curvedata • Show schema
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{'Ciso': '159120cs', 'Clabel': '159120cs1', 'Cnumber': 1, 'abc_quality': 1.0645470218174347, 'absD': 886202132400, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 13260, 'ainvs': [0, 0, 0, -10968, -444433], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 159120, 'degree': 221184, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1317851158117119343314740819', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-337770946363392, 2051393825], 'lmfdb_iso': '159120.r', 'lmfdb_label': '159120.r3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -10968, 444433], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0-6.a.1.3', '102.24.0.?', '204.48.0.?', '780.48.0.?', '4420.6.0.?', '13260.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.4680285313733200014792447725', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.62608298345803607501025206552', 'prec': 103}, 'szpiro_ratio': 3.3005668006339284, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 4, 0], 'aplist': [0, 0, -1, -2, 0, 1, -1, 4, 0, 6, -8, 2, 6, 4, 12, 6, 6, -10, 4, 0, 2, 10, -12, -6, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 159120, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '159120.r', 'trace_hash': 273777785487028224}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.10397859361794995783930105826', 'prec': 103}, 'conductor': 159120, 'gens': [[497, 2665, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '4.4680285313733200014792447725', 'prec': 100}], 'lmfdb_label': '159120.r3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.23317395908828541041291761896', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2509674118784067860863228917077555601', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[121, 0, 1]], 'xcoord_integral_points': [121, 10261]}
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lmfdb_label 159120.r3 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 7120993
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [6]}
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id: 7120992
{'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '159120.r3', 'torsion': [2, 2]}
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id: 7120994
{'degree': 4, 'field': [-51, 0, 54, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [4]}
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id: 7120995
{'degree': 4, 'field': [169, 0, -25, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [2, 6]}
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id: 7120996
{'degree': 6, 'field': [722473, -15300, 27, -1700, -9, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [6]}
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id: 7120999
{'degree': 8, 'field': [676, -1352, 1352, -1352, 628, 44, 8, -4, 1], 'lmfdb_label': '159120.r3', 'torsion': [12]}
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id: 7120997
{'degree': 8, 'field': [38025, 0, -5022, 0, 1527, 0, -54, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [2, 4]}
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id: 7120998
{'degree': 8, 'field': [350029, -70000, 75286, -10732, 5767, -484, 166, -4, 1], 'lmfdb_label': '159120.r3', 'torsion': [2, 4]}
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id: 7121001
{'degree': 12, 'field': [722500, 0, 0, 0, 0, 0, 44200, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [2, 6]}
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id: 7121000
{'degree': 12, 'field': [522007695001, -3684755100, 23842497, -2456518700, 6502506, 35700, 4334993, 0, 6, -3400, -3, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [3, 6]}
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id: 7121002
{'degree': 16, 'field': [6765201, 0, -10773383616, 0, -318785915628, 0, 165128209632, 0, 1604748150, 0, 9831168, 0, 90612, 0, 96, 0, 1], 'lmfdb_label': '159120.r3', 'torsion': [8]}
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id: 7121003
{'degree': 16, 'field': [77228944, -11881376, 913952, 843648, -11878672, 873392, 10816, -100464, 434476, 7560, -800, 2584, 1724, -216, 8, -4, 1], 'lmfdb_label': '159120.r3', 'torsion': [2, 12]}
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id: 7121004
{'degree': 16, 'field': [1110155761, -27721408, 346112, 54802644, -27291754, -801812, 1381192, -945612, 219127, 20508, -13016, 4748, -670, -84, 32, -8, 1], 'lmfdb_label': '159120.r3', 'torsion': [2, 12]}
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id: 7121005
{'degree': 18, 'field': [38614472, -231686832, 695060496, -1233149736, 1377097176, -910401648, 364924404, -132732600, 128291280, -61803508, 18315492, -6271824, 1116864, -27480, 8616, -1488, 18, -6, 1], 'lmfdb_label': '159120.r3', 'torsion': [18]}
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ec_localdata • Show schema
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id: 3936177
{'conductor': 159120, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '159120.r3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 3936178
{'conductor': 159120, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '159120.r3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 3936179
{'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '159120.r3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 3936180
{'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '159120.r3', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
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id: 3936181
{'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '159120.r3', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2693635
{'adelic_gens': [[1101, 5522, 7714, 12139], [1, 0, 12, 1], [11, 2, 13210, 13251], [1, 6, 6, 37], [13249, 12, 13248, 13], [1, 12, 0, 1], [11221, 12, 1026, 73], [8852, 11, 8805, 13228], [5470, 3, 7773, 13252], [7957, 12, 7962, 73]], 'adelic_image': '13260.96.1.?', 'conductor': 159120, 'lmfdb_label': '159120.r3', 'prime': 0}
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id: 606646
{'conductor': 159120, 'elladic_image': '2.3.0.1', 'lmfdb_label': '159120.r3', 'modell_image': '2B', 'prime': 2}
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id: 606647
{'conductor': 159120, 'elladic_image': '3.4.0.1', 'lmfdb_label': '159120.r3', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 159120.r does not appear in ec_padic