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ec_curvedata • Show schema
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{'Ciso': '33a', 'Clabel': '33a3', 'Cnumber': 3, 'abc_quality': 1.0091329432672695, 'absD': 395307, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [1, 1, 0, -146, 621], 'analytic_rank': 0, 'bad_primes': [3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 33, 'degree': 6, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.012632067116688598242446120205', 'prec': 110}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [347873904937, 395307], 'lmfdb_iso': '33.a', 'lmfdb_label': '33.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -146, 621], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '12.24.0-12.h.1.2', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.012632067116688598242446120205', 'prec': 110}, 'szpiro_ratio': 7.600471453800636, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, -1, -1, -2, -1, 4, -3, 1, -2, 1, 1, -2, 4, 2, -1, -2, 1, 0, 2], 'aplist': [1, -1, -2, 4, 1, -2, -2, 0, 8, -6, -8, 6, -2, 0, 8, 6, -4, 6, -4, 0, -14, -4, 12, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 33, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '33.a', 'trace_hash': 2215180138185436427}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.0255859771174331474340959251', 'prec': 100}, 'conductor': 33, 'gens': [], 'heights': [], 'lmfdb_label': '33.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.9893565909709744778226018631', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.74733914774274361945565046577174532389', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[4, 9, 1]], 'xcoord_integral_points': [4]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 0], '3': [0, 0], '11': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '33.a1'}
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ec_torsion_growth • Show schema
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id: 909
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '33.a1', 'torsion': [2, 4]}
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id: 910
{'degree': 4, 'field': [3, 0, 1, 0, 1], 'lmfdb_label': '33.a1', 'torsion': [8]}
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id: 914
{'degree': 8, 'field': [-1, 1, 2, -7, 7, -7, 7, -4, 1], 'lmfdb_label': '33.a1', 'torsion': [12]}
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id: 911
{'degree': 8, 'field': [9, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '33.a1', 'torsion': [4, 4]}
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id: 913
{'degree': 8, 'field': [36, 0, -252, 0, 165, 0, -24, 0, 1], 'lmfdb_label': '33.a1', 'torsion': [2, 8]}
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id: 912
{'degree': 8, 'field': [253, -242, 146, -2, -5, 2, 8, -4, 1], 'lmfdb_label': '33.a1', 'torsion': [2, 8]}
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id: 916
{'degree': 16, 'field': [9, 0, -99, 0, 180, 0, -162, 0, 120, 0, -72, 0, 25, 0, -5, 0, 1], 'lmfdb_label': '33.a1', 'torsion': [2, 12]}
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id: 915
{'degree': 16, 'field': [1296, 0, 432, 0, -1008, 0, -180, 0, 603, 0, -168, 0, 104, 0, 20, 0, 1], 'lmfdb_label': '33.a1', 'torsion': [16]}
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ec_localdata • Show schema
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id: 116
{'conductor': 33, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '33.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 117
{'conductor': 33, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '33.a1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1665941
{'adelic_gens': [[235, 234, 178, 43], [232, 107, 235, 0], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 258, 259], [257, 8, 256, 9], [184, 3, 181, 2], [145, 8, 52, 33]], 'adelic_image': '264.48.0.?', 'conductor': 33, 'lmfdb_label': '33.a1', 'prime': 0}
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id: 71
{'conductor': 33, 'elladic_image': '4.12.0.7', 'lmfdb_label': '33.a1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 33.a does not appear in ec_padic