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ec_curvedata • Show schema
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{'Ciso': '20a', 'Clabel': '20a1', 'Cnumber': 1, 'abc_quality': 0.8396384887826309, 'absD': 6400, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, 1, 0, 4, 4], 'analytic_rank': 0, 'bad_primes': [2, 5], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 20, 'degree': 1, 'elladic_images': ['8.12.0.37', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.58337650523554731646541001985', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [21296, 25], 'lmfdb_iso': '20.a', 'lmfdb_label': '20.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 4, 4], '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.a.1', '6.24.0-6.a.1.4', '8.12.0-4.a.1.1', '12.48.0-12.d.1.11', '20.12.0.d.1', '24.96.0-24.bh.1.8', '40.48.0-40.bc.1.1', '60.96.1-60.h.1.7', '120.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0454746256088441894102314342', 'prec': 103}, 'szpiro_ratio': 5.18724658047375, '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': '3.2115478284400650875837220976', 'prec': 100}, 'conductor': 20, 'gens': [], 'heights': [], 'lmfdb_label': '20.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.8243751419591137994837895490', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.47072919032651896658063159150721550180', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [[4, 10, 1]], 'xcoord_integral_points': [-1, 0, 4]}
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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.a4'}
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ec_torsion_growth • Show schema
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id: 346
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '20.a4', 'torsion': [2, 6]}
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id: 347
{'degree': 4, 'field': [-1, 0, -1, 0, 1], 'lmfdb_label': '20.a4', 'torsion': [12]}
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id: 348
{'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '20.a4', 'torsion': [3, 6]}
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id: 349
{'degree': 8, 'field': [1, -2, 2, 2, -2, 2, 2, -2, 1], 'lmfdb_label': '20.a4', 'torsion': [2, 12]}
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id: 350
{'degree': 8, 'field': [2, -8, 8, 4, -8, 0, 6, -4, 1], 'lmfdb_label': '20.a4', 'torsion': [2, 12]}
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id: 351
{'degree': 9, 'field': [-1, 6, -9, 1, 3, 0, -2, 3, -3, 1], 'lmfdb_label': '20.a4', 'torsion': [18]}
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id: 352
{'degree': 12, 'field': [9, 0, 21, 0, 46, 0, 1, 0, -6, 0, 1, 0, 1], 'lmfdb_label': '20.a4', 'torsion': [6, 6]}
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id: 354
{'degree': 16, 'field': [1, 0, 16, 0, -10, 0, -36, 0, 59, 0, -36, 0, -10, 0, -4, 0, 1], 'lmfdb_label': '20.a4', 'torsion': [24]}
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id: 353
{'degree': 16, 'field': [1, 4, 2, -8, 2, -36, 126, -204, 199, -128, 74, -68, 72, -56, 28, -8, 1], 'lmfdb_label': '20.a4', 'torsion': [4, 12]}
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id: 355
{'degree': 18, 'field': [1, 0, 18, 0, 63, 0, 51, 0, 15, 0, -24, 0, -16, 0, -3, 0, 3, 0, 1], 'lmfdb_label': '20.a4', 'torsion': [2, 18]}
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ec_localdata • Show schema
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id: 38
{'conductor': 20, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '20.a4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
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id: 39
{'conductor': 20, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '20.a4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1665915
{'adelic_gens': [[97, 24, 96, 25], [1, 0, 24, 1], [99, 4, 71, 65], [13, 24, 12, 13], [15, 16, 74, 95], [61, 24, 6, 25], [1, 24, 0, 1], [15, 22, 14, 83], [99, 16, 46, 3]], 'adelic_image': '120.384.9.?', 'conductor': 20, 'lmfdb_label': '20.a4', 'prime': 0}
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id: 36
{'conductor': 20, 'elladic_image': '8.12.0.37', 'lmfdb_label': '20.a4', 'modell_image': '2B', 'prime': 2}
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id: 37
{'conductor': 20, 'elladic_image': '3.8.0.1', 'lmfdb_label': '20.a4', 'modell_image': '3B.1.1', 'prime': 3}
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lmfdb_iso 20.a does not appear in ec_padic