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ec_curvedata • Show schema
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{'Ciso': '156816y', 'Clabel': '156816y1', 'Cnumber': 1, 'abc_quality': 1.2193606426954804, 'absD': 5916222801789696, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 22, 'ainvs': [0, 0, 0, 2904, -3700180], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 156816, 'degree': 950400, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7053301042748170884322789318', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1], 'jinv': [73728, 161051], 'lmfdb_iso': '156816.v', 'lmfdb_label': '156816.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 24, -2780], 'min_quad_twist_disc': 44, 'modell_images': [], 'modm_images': ['22.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.8786225130999744785643021463', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9801], [3, 8, 1936], [11, 72, 1296]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32191974872036828700859601713', 'prec': 107}, 'szpiro_ratio': 3.658911424777221, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 6, 0], 'aplist': [0, 0, -2, 4, 0, -4, 4, 6, 3, -8, 5, 7, 2, 4, -11, -1, 3, 8, 12, -13, 0, -14, -4, 11, 1], 'class_deg': 1, 'class_size': 1, 'conductor': 156816, 'isogeny_matrix': [[1]], 'lmfdb_iso': '156816.v', 'trace_hash': 1716008729025091445}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.033019393492246203234211698021', 'prec': 107}, 'conductor': 156816, 'gens': [[376178, 230197418, 23]], 'heights': [{'__RealLiteral__': 0, 'data': '9.8786225130999744785643021463', 'prec': 100}], 'lmfdb_label': '156816.v1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19770746010305189596229672479', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.8123094655272938387702136330824553536', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
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lmfdb_label 156816.v1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 7026792
{'degree': 3, 'field': [-10, 6, 0, 1], 'lmfdb_label': '156816.v1', 'torsion': [2]}
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id: 7026793
{'degree': 6, 'field': [44, 0, 144, 0, -24, 0, 1], 'lmfdb_label': '156816.v1', 'torsion': [2, 2]}
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id: 7026794
{'degree': 8, 'field': [-1452, 0, -4224, 0, -396, 0, -11, 0, 1], 'lmfdb_label': '156816.v1', 'torsion': [3]}
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id: 7026795
{'degree': 12, 'field': [-4735, -15948, -6402, 6176, 2079, -2856, -1900, -288, 63, -12, -18, 0, 1], 'lmfdb_label': '156816.v1', 'torsion': [4]}
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ec_localdata • Show schema
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id: 3878945
{'conductor': 156816, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '156816.v1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 3878946
{'conductor': 156816, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '156816.v1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 3878947
{'conductor': 156816, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '156816.v1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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{'adelic_gens': [[1, 1, 21, 0], [1, 2, 0, 1], [1, 0, 2, 1], [21, 2, 20, 3], [13, 2, 13, 3]], 'adelic_image': '22.2.0.?', 'conductor': 156816, 'lmfdb_label': '156816.v1', 'prime': 0}
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lmfdb_iso 156816.v does not appear in ec_padic
