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ec_curvedata • Show schema
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{'Ciso': '81120u', 'Clabel': '81120u3', 'Cnumber': 3, 'abc_quality': 0.8851019596995587, 'absD': 1058753217400320, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 1, 0, -36560, 2176188], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 81120, 'degree': 258048, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5996771257102330092433846543', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 48, 'isogeny_degrees': [1, 2, 4], 'jinv': [2186875592, 428415], 'lmfdb_iso': '81120.bw', 'lmfdb_label': '81120.bw2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -216, -924], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '104.24.0.?', '120.24.0.?', '780.12.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '19.099534960810457449147331217', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.20265793844049434084628315758', 'prec': 107}, 'szpiro_ratio': 3.815902615204418, '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, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, -4, 0], 'aplist': [0, 1, 1, 0, 0, 0, 2, -4, -4, -6, 8, 6, 2, -4, 0, 6, 0, -2, 8, 0, -6, 4, -12, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 81120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '81120.bw', 'trace_hash': 68482071992267504}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.040788534614254310698718270401', 'prec': 107}, 'conductor': 81120, 'gens': [[171715747, 844214539364, 1023]], 'heights': [{'__RealLiteral__': 0, 'data': '19.099534960810457449147331217', 'prec': 100}], 'lmfdb_label': '81120.bw2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.46618747180536445643415167601', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.9039639160383978604292959431204764103', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[147, 0, 1]], 'xcoord_integral_points': [147]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': 'a', '17': [1, 0], '19': [1, 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': '81120.bw2'}
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ec_torsion_growth • Show schema
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id: 3814091
{'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [4]}
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id: 3814090
{'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [2, 2]}
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id: 3814092
{'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [4]}
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id: 3814093
{'degree': 4, 'field': [1, 0, -28, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [2, 4]}
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id: 3814094
{'degree': 4, 'field': [120, 0, -60, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [8]}
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id: 3814098
{'degree': 8, 'field': [-727, -1616, 1460, 108, 42, -48, 4, -4, 1], 'lmfdb_label': '81120.bw2', 'torsion': [6]}
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id: 3814096
{'degree': 8, 'field': [900, 0, 0, 0, -44, 0, 0, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [8]}
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id: 3814097
{'degree': 8, 'field': [26776, -23040, -20336, 3840, 2916, -120, -116, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [2, 8]}
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id: 3814095
{'degree': 8, 'field': [99376, 69120, 26576, 6720, 156, -240, -4, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [2, 4]}
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id: 3814103
{'degree': 16, 'field': [9, 0, -37488, 0, -99740, 0, -74976, 0, 30, 0, 12496, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [12]}
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id: 3814100
{'degree': 16, 'field': [676, 0, 3536, 0, 5768, 0, 4704, 0, 1808, 0, 168, 0, -28, 0, 8, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [2, 8]}
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id: 3814101
{'degree': 16, 'field': [608400, 0, -2433600, 0, 1029600, 0, 93600, 0, 12840, 0, -11280, 0, 2280, 0, -120, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [16]}
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id: 3814104
{'degree': 16, 'field': [19307236, 0, -5940688, 0, 456976, 0, 158184, 0, 135876, 0, -8424, 0, 676, 0, -52, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [12]}
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id: 3814102
{'degree': 16, 'field': [25979409, 0, -5901228, 0, 4332460, 0, -141756, 0, 150090, 0, -13004, 0, 1068, 0, -60, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [2, 6]}
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id: 3814099
{'degree': 16, 'field': [38576521, -53663040, 37324800, -18267600, 10551226, -5989320, 2448000, -481440, 27231, -7320, 7200, 1440, -74, -120, 0, 0, 1], 'lmfdb_label': '81120.bw2', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 1973786
{'conductor': 81120, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81120.bw2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 1973787
{'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '81120.bw2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 1973788
{'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '81120.bw2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 1973789
{'conductor': 81120, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '81120.bw2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2198688
{'adelic_gens': [[1256, 3, 5, 2], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [479, 1552, 356, 1527], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [1048, 3, 1045, 2], [192, 967, 983, 996], [1368, 593, 187, 174]], 'adelic_image': '1560.48.0.?', 'conductor': 81120, 'lmfdb_label': '81120.bw2', 'prime': 0}
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id: 332677
{'conductor': 81120, 'elladic_image': '8.12.0.6', 'lmfdb_label': '81120.bw2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 4180064
{'lmfdb_iso': '81120.bw', 'p': 17, 'prec': 20, 'unit': 165095652235518519830222, 'val': 1}
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id: 4180056
{'lmfdb_iso': '81120.bw', 'p': 19, 'prec': 20, 'unit': 1489099981758105629182835, 'val': 1}
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id: 4180068
{'lmfdb_iso': '81120.bw', 'p': 23, 'prec': 20, 'unit': 49764417789484324600827851, 'val': 1}
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id: 4180062
{'lmfdb_iso': '81120.bw', 'p': 29, 'prec': 20, 'unit': 3848273353872671589368133299, 'val': 1}
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id: 4180071
{'lmfdb_iso': '81120.bw', 'p': 31, 'prec': 20, 'unit': 18628536080268429385073559457, 'val': 1}
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id: 4180059
{'lmfdb_iso': '81120.bw', 'p': 37, 'prec': 20, 'unit': 370950069750158456082518338672, 'val': 1}
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id: 4180060
{'lmfdb_iso': '81120.bw', 'p': 41, 'prec': 20, 'unit': 3354511284011915365225985166586, 'val': 1}
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id: 4180061
{'lmfdb_iso': '81120.bw', 'p': 43, 'prec': 20, 'unit': 5034158582551802661095637324802, 'val': 1}
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id: 4180066
{'lmfdb_iso': '81120.bw', 'p': 53, 'prec': 20, 'unit': 473344920501198953333331759518838, 'val': 1}
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id: 4180070
{'lmfdb_iso': '81120.bw', 'p': 61, 'prec': 20, 'unit': 1070399459931678539220975264296440, 'val': 1}
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id: 4180058
{'lmfdb_iso': '81120.bw', 'p': 67, 'prec': 20, 'unit': 32788108252455909816210092884434469, 'val': 1}
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id: 4180067
{'lmfdb_iso': '81120.bw', 'p': 73, 'prec': 20, 'unit': 186486849617483580728611770081853742, 'val': 1}
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id: 4180063
{'lmfdb_iso': '81120.bw', 'p': 79, 'prec': 20, 'unit': 316772977926817939892724045634988911, 'val': 1}
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id: 4180065
{'lmfdb_iso': '81120.bw', 'p': 83, 'prec': 20, 'unit': 2160586418474136486969719565944581021, 'val': 1}
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id: 4180069
{'lmfdb_iso': '81120.bw', 'p': 89, 'prec': 20, 'unit': 6900936188487357318005885166541035075, 'val': 1}
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id: 4180057
{'lmfdb_iso': '81120.bw', 'p': 97, 'prec': 20, 'unit': 35285348074718544667456201443386705141, 'val': 1}