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ec_curvedata • Show schema
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{'Ciso': '20a', 'Clabel': '20a2', 'Cnumber': 2, 'abc_quality': 0.9562146657916117, 'absD': 80, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, 1, 0, -1, 0], 'analytic_rank': 0, 'bad_primes': [2, 5], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 20, 'degree': 2, 'elladic_images': ['8.12.0.22', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.92995009551551997117402608057', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [16384, 5], 'lmfdb_iso': '20.a', 'lmfdb_label': '20.a3', 'lmfdb_number': 3, 'manin_constant': 2, 'min_quad_twist_ainvs': [0, 1, 0, -1, 0], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.b.1', '6.24.0-6.a.1.4', '8.12.0-4.b.1.2', '10.6.0.a.1', '12.48.0-12.f.1.8', '20.24.0.e.1', '24.96.0-24.bq.1.2', '30.48.0-30.a.1.4', '40.48.0-20.e.1.6', '60.192.3-60.bk.1.8', '120.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1609991557021684076464367877', 'prec': 103}, 'szpiro_ratio': 4.164807836875665, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, -6, 0, -4, 0], 'aplist': [0, -2, -1, 2, 0, 2, -6, -4, 6, 6, -4, 2, 6, -10, -6, -6, 12, 2, 2, -12, 2, 8, 6, -6, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 20, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '20.a', 'trace_hash': 12896406231020588}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '6.4230956568801301751674441952', 'prec': 100}, 'conductor': 20, 'gens': [], 'heights': [], 'lmfdb_label': '20.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '5.6487502839182275989675790981', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.47072919032651896658063159150721550180', 'prec': 133}, 'tamagawa_product': 3, 'torsion_generators': [[-1, 1, 1]], 'xcoord_integral_points': [-1, 0, 1]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '20.a3'}
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ec_torsion_growth • Show schema
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id: 356
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '20.a3', 'torsion': [2, 6]}
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id: 357
{'degree': 4, 'field': [2, 0, 0, -2, 1], 'lmfdb_label': '20.a3', 'torsion': [12]}
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id: 358
{'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '20.a3', 'torsion': [3, 6]}
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id: 359
{'degree': 8, 'field': [-4, 16, -16, -8, 14, 4, -4, -2, 1], 'lmfdb_label': '20.a3', 'torsion': [2, 12]}
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id: 360
{'degree': 8, 'field': [1, -2, 2, 2, -2, 2, 2, -2, 1], 'lmfdb_label': '20.a3', 'torsion': [2, 12]}
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id: 361
{'degree': 9, 'field': [-1, 6, -9, 1, 3, 0, -2, 3, -3, 1], 'lmfdb_label': '20.a3', 'torsion': [18]}
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id: 362
{'degree': 12, 'field': [1, -1, 1, 10, -5, -1, 26, -1, -5, 10, 1, -1, 1], 'lmfdb_label': '20.a3', 'torsion': [6, 6]}
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id: 364
{'degree': 16, 'field': [1, -8, 24, -36, 42, -60, 56, -16, 4, 0, -8, -12, 10, -4, 8, 0, 1], 'lmfdb_label': '20.a3', 'torsion': [24]}
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id: 363
{'degree': 16, 'field': [1, -6, 18, -36, 47, -30, -18, 72, -95, 72, -18, -30, 47, -36, 18, -6, 1], 'lmfdb_label': '20.a3', 'torsion': [4, 12]}
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id: 365
{'degree': 18, 'field': [1, 6, -30, -4, 51, 24, -83, 138, -201, 62, 102, -132, 166, -168, 93, -34, 15, -6, 1], 'lmfdb_label': '20.a3', 'torsion': [2, 18]}
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ec_localdata • Show schema
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id: 40
{'conductor': 20, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '20.a3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
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id: 41
{'conductor': 20, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '20.a3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1665914
{'adelic_gens': [[1, 12, 12, 25], [97, 24, 96, 25], [105, 106, 14, 35], [1, 0, 24, 1], [21, 4, 20, 101], [1, 24, 0, 1], [7, 24, 12, 7], [61, 24, 72, 49], [81, 4, 100, 81], [112, 3, 117, 34]], 'adelic_image': '120.384.9.?', 'conductor': 20, 'lmfdb_label': '20.a3', 'prime': 0}
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id: 34
{'conductor': 20, 'elladic_image': '8.12.0.22', 'lmfdb_label': '20.a3', 'modell_image': '2B', 'prime': 2}
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id: 35
{'conductor': 20, 'elladic_image': '3.8.0.1', 'lmfdb_label': '20.a3', 'modell_image': '3B.1.1', 'prime': 3}
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lmfdb_iso 20.a does not appear in ec_padic