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ec_curvedata • Show schema
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{'Ciso': '33135a', 'Clabel': '33135a2', 'Cnumber': 2, 'abc_quality': 0.9622954410890624, 'absD': 2425323449025, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 11280, 'ainvs': [1, 1, 1, -11091, -447912], 'analytic_rank': 0, 'bad_primes': [3, 5, 47], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 33135, 'degree': 51520, 'elladic_images': ['16.48.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1762226384922128512582627770', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13997521, 225], 'lmfdb_iso': '33135.d', 'lmfdb_label': '33135.d6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5, 2], 'min_quad_twist_disc': -47, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.i.1', '16.48.0.d.2', '24.48.0.bb.2', '40.48.0.bd.1', '48.96.1.n.1', '60.24.0.c.1', '80.192.5.?', '120.96.1.?', '188.24.0.?', '240.384.13.?', '376.48.0.?', '752.96.0.?', '1128.96.0.?', '1880.96.0.?', '2256.192.1.?', '2820.48.0.?', '3760.384.5.?', '5640.192.1.?', '11280.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2209], [3, 4, 11045], [5, 6, 6627], [47, 1106, 15]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74885116236281644215221255789', 'prec': 107}, 'szpiro_ratio': 3.800342405388077, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, -1, -1, 1, 0, 3, 1, 1, 4, 1, 2, 0, 1, -1, 2, -1, -4, 1], 'aplist': [-1, -1, -1, 0, 4, 2, 2, -4, 0, 2, 0, -10, -10, -4, 0, -10, -4, -2, -12, -8, -10, 0, 12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 33135, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '33135.d', 'trace_hash': 246767084640461369}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.095136243090107621351776288601', 'prec': 107}, 'conductor': 33135, 'gens': [], 'heights': [], 'lmfdb_label': '33135.d6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.46567171631966582947733866179', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.46567171631966582947733866179439606309', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-67, 33, 1], [121, -61, 1]], 'xcoord_integral_points': [-67, 121]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [8, 0], '3': [0, 0], '5': [0, 0], '47': 'a'}, 'iwp0': 3, 'lmfdb_label': '33135.d6'}
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ec_torsion_growth • Show schema
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id: 1647090
{'degree': 2, 'field': [12, -1, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 4]}
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id: 1647091
{'degree': 4, 'field': [64, 0, -31, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 4]}
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id: 1647093
{'degree': 4, 'field': [169, 0, 21, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 8]}
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id: 1647092
{'degree': 4, 'field': [2554, 86, -85, -2, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 4]}
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id: 1647097
{'degree': 8, 'field': [-57165, -3, -15043, 540, -615, -31, -3, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 6]}
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id: 1647095
{'degree': 8, 'field': [20736, 0, 3312, 0, 385, 0, 23, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 8]}
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id: 1647096
{'degree': 8, 'field': [36661, -2233, 8095, -658, 789, -62, 40, -2, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 16]}
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id: 1647094
{'degree': 8, 'field': [57664, 7920, -7214, -1382, 617, 86, -24, -4, 1], 'lmfdb_label': '33135.d6', 'torsion': [4, 4]}
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id: 1647098
{'degree': 16, 'field': [-41933759, 58084320, 27906462, -71794680, 20056360, 21481860, -12045978, -1611480, 2020089, -3300, -161862, 3000, 6640, -60, -132, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 8]}
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id: 1647100
{'degree': 16, 'field': [210946576, 0, -177403492, 0, 62659769, 0, -12047688, 0, 1390904, 0, -98838, 0, 4232, 0, -100, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [4, 8]}
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id: 1647102
{'degree': 16, 'field': [363093025, 0, 245792032, 0, 73753000, 0, 12591369, 0, 1337232, 0, 90855, 0, 3865, 0, 94, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 12]}
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id: 1647101
{'degree': 16, 'field': [429981696, 0, 68677632, 0, 7983360, 0, 798192, 0, 72049, 0, 5543, 0, 385, 0, 23, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 16]}
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id: 1647099
{'degree': 16, 'field': [11500956385636, 0, -2585228671992, 0, 240988454800, 0, -12126015372, 0, 360799029, 0, -6510108, 0, 69790, 0, -408, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 775489
{'conductor': 33135, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '33135.d6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 775490
{'conductor': 33135, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '33135.d6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 775491
{'conductor': 33135, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '33135.d6', 'prime': 47, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1885358
{'adelic_gens': [[4325, 6016, 4324, 4513], [4319, 0, 0, 11279], [3855, 8648, 10528, 10529], [1, 16, 0, 1], [11265, 16, 11264, 17], [3761, 6016, 6486, 2257], [1, 16, 4, 65], [8461, 8648, 3290, 8837], [1, 0, 16, 1]], 'adelic_image': '11280.768.13.?', 'conductor': 33135, 'lmfdb_label': '33135.d6', 'prime': 0}
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id: 147795
{'conductor': 33135, 'elladic_image': '16.48.0.3', 'lmfdb_label': '33135.d6', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 33135.d does not appear in ec_padic