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ec_curvedata • Show schema
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{'Ciso': '19a', 'Clabel': '19a2', 'Cnumber': 2, 'abc_quality': 1.104947099482495, 'absD': 19, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 1026, 'ainvs': [0, 1, 1, -769, -8470], 'analytic_rank': 0, 'bad_primes': [19], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 19, 'degree': 3, 'elladic_images': ['27.72.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.033439156991317803520094883584', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [-50357871050752, 19], 'lmfdb_iso': '19.a', 'lmfdb_label': '19.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -769, -8470], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.2'], 'modm_images': ['3.8.0-3.a.1.1', '9.24.0-9.a.1.1', '27.72.0-27.a.1.1', '38.2.0.a.1', '114.16.0.?', '171.72.0.?', '342.144.3.?', '513.648.16.?', '1026.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.033439156991317803520094883584', 'prec': 107}, 'szpiro_ratio': 10.715174019054395, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -2, -2, 3, 0, -1, 0, 1, 0, 3, 4, -4, 0, -6, 4, -3, 0, 1, -6], 'aplist': [0, -2, 3, -1, 3, -4, -3, 1, 0, 6, -4, 2, -6, -1, -3, 12, -6, -1, -4, 6, -7, 8, 12, 12, 8], 'class_deg': 9, 'class_size': 3, 'conductor': 19, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '19.a', 'trace_hash': 409437620317032020}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.93530900844051168958806055461', 'prec': 103}, 'conductor': 19, 'gens': [], 'heights': [], 'lmfdb_label': '19.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.45325324449610360357883918706', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.45325324449610360357883918706482153450', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 3, 0], '3': [0, 2], '19': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '19.a1'}
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ec_torsion_growth • Show schema
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id: 319
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '19.a1', 'torsion': [3]}
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id: 321
{'degree': 3, 'field': [-12, -6, -1, 1], 'lmfdb_label': '19.a1', 'torsion': [3]}
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id: 320
{'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [2]}
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id: 322
{'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '19.a1', 'torsion': [2, 2]}
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id: 326
{'degree': 6, 'field': [4, -4, 4, -4, 2, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [6]}
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id: 323
{'degree': 6, 'field': [12, 6, -5, -3, 4, -3, 1], 'lmfdb_label': '19.a1', 'torsion': [3, 3]}
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id: 325
{'degree': 6, 'field': [19, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [9]}
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id: 324
{'degree': 6, 'field': [6859, 0, 0, -19, 0, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [9]}
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id: 327
{'degree': 9, 'field': [-18, 68, -94, 69, -35, 10, -1, 4, -3, 1], 'lmfdb_label': '19.a1', 'torsion': [6]}
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id: 328
{'degree': 12, 'field': [-2, -4, -4, -4, 6, 8, -4, 0, -4, -10, -2, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [4]}
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id: 329
{'degree': 12, 'field': [1, -3, 5, -6, 3, 9, -14, 9, 3, -6, 5, -3, 1], 'lmfdb_label': '19.a1', 'torsion': [2, 6]}
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id: 334
{'degree': 18, 'field': [324, -1224, 2156, -2992, 4226, -4834, 5135, -4799, 4227, -3044, 2285, -1195, 738, -295, 147, -42, 17, -3, 1], 'lmfdb_label': '19.a1', 'torsion': [2, 6]}
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id: 331
{'degree': 18, 'field': [324, -1224, 2932, -3908, 3514, -1906, 827, -675, 931, -756, 285, -31, -6, 21, 3, -10, 5, -3, 1], 'lmfdb_label': '19.a1', 'torsion': [3, 6]}
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id: 333
{'degree': 18, 'field': [6859, 0, 0, 3819, 0, 0, 608, 0, 0, 1, 0, 0, 40, 0, 0, -5, 0, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [18]}
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id: 330
{'degree': 18, 'field': [19683, 0, 0, -13851, 0, 0, 2700, 0, 0, -171, 0, 0, 100, 0, 0, -19, 0, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [3, 9]}
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id: 332
{'degree': 18, 'field': [47045881, 0, 0, -11337927, 0, 0, 1454108, 0, 0, -103607, 0, 0, 4180, 0, 0, -95, 0, 0, 1], 'lmfdb_label': '19.a1', 'torsion': [18]}
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ec_localdata • Show schema
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{'conductor': 19, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '19.a1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1665909
{'adelic_gens': [[31, 36, 334, 421], [1, 54, 0, 1], [937, 75, 627, 92], [973, 54, 972, 55], [1, 0, 54, 1], [28, 27, 729, 703], [70, 45, 385, 472]], 'adelic_image': '1026.1296.43.?', 'conductor': 19, 'lmfdb_label': '19.a1', 'prime': 0}
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id: 27
{'conductor': 19, 'elladic_image': '27.72.0.2', 'lmfdb_label': '19.a1', 'modell_image': '3B.1.2', 'prime': 3}
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lmfdb_iso 19.a does not appear in ec_padic