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ec_curvedata • Show schema
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{'Ciso': '155232ds', 'Clabel': '155232ds2', 'Cnumber': 2, 'abc_quality': 1.0353155241318501, 'absD': 442173235965432069864826368, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 616, 'ainvs': [0, 0, 0, -720826995, 7379919337574], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 155232, 'degree': 61931520, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9286541330148405454693942315', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 63, 'isogeny_degrees': [1, 2], 'jinv': [943259332190261813000, 10069472554261659], 'lmfdb_iso': '155232.cl', 'lmfdb_label': '155232.cl1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1634528, -796336632], 'min_quad_twist_disc': -84, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '88.6.0.?', '616.12.0.?'], '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': '17.586091537036832604036234622', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 4851], [3, 6, 17248], [5, 2, 14112], [7, 32, 3168], [11, 12, 14112]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8865325287331700651561711502', 'prec': 100}, 'szpiro_ratio': 6.090797731555605, '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, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 4, 0, 6, 0], 'aplist': [0, 0, 0, 0, -1, 2, 4, 6, 4, 2, -10, -6, -12, -12, -6, 6, 0, -6, -4, 8, -8, 16, -2, 10, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 155232, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '155232.cl', 'trace_hash': 1718591437774628527}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00038691394034639726880133550909', 'prec': 113}, 'conductor': 155232, 'gens': [[-1105631891, 24570710170398, 205]], 'heights': [{'__RealLiteral__': 0, 'data': '17.586091537036832604036234622', 'prec': 100}], 'lmfdb_label': '155232.cl1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.053082638939279322225802390427', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.4681291793091353383642264482180709285', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[14266, 0, 1]], 'xcoord_integral_points': [14266]}
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lmfdb_label 155232.cl1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 6962317
{'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '155232.cl1', 'torsion': [2, 2]}
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id: 6962318
{'degree': 4, 'field': [46, 19, -1, -1, 1], 'lmfdb_label': '155232.cl1', 'torsion': [4]}
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id: 6962321
{'degree': 8, 'field': [-156134, -92436, -17828, 2944, 1236, -8, -50, 0, 1], 'lmfdb_label': '155232.cl1', 'torsion': [6]}
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id: 6962320
{'degree': 8, 'field': [7744, 11616, 8382, 2904, 203, -132, -30, 0, 1], 'lmfdb_label': '155232.cl1', 'torsion': [2, 4]}
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id: 6962319
{'degree': 8, 'field': [53361, 0, -71148, 0, -2288, 0, -44, 0, 1], 'lmfdb_label': '155232.cl1', 'torsion': [2, 4]}
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id: 6962323
{'degree': 16, 'field': [-8213551983, 13543250616, 1501715868, -2021700876, -29802114, 26253468, 27972612, -4290804, -637040, -115816, 3676, 8068, -178, -68, -8, -4, 1], 'lmfdb_label': '155232.cl1', 'torsion': [2, 6]}
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id: 6962322
{'degree': 16, 'field': [1929187036, -236203520, -845776848, -159779200, 270784836, 8487192, -19517372, -3061912, 1583367, 288676, -55706, -10248, 1995, 280, -42, -4, 1], 'lmfdb_label': '155232.cl1', 'torsion': [8]}
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ec_localdata • Show schema
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id: 3839796
{'conductor': 155232, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '155232.cl1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 3839797
{'conductor': 155232, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '155232.cl1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 3839798
{'conductor': 155232, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '155232.cl1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 3839799
{'conductor': 155232, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '155232.cl1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2669392
{'adelic_gens': [[1, 0, 4, 1], [353, 4, 90, 9], [3, 4, 8, 11], [613, 4, 612, 5], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 307, 0], [540, 81, 385, 232], [114, 1, 559, 0]], 'adelic_image': '616.12.0.?', 'conductor': 155232, 'lmfdb_label': '155232.cl1', 'prime': 0}
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id: 593452
{'conductor': 155232, 'elladic_image': '2.3.0.1', 'lmfdb_label': '155232.cl1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 155232.cl does not appear in ec_padic