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ec_curvedata • Show schema
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{'Ciso': '195a', 'Clabel': '195a6', 'Cnumber': 6, 'abc_quality': 1.0149811194984983, 'absD': 183539412225, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 6240, 'ainvs': [1, 0, 0, 605, -19750], 'analytic_rank': 0, 'bad_primes': [3, 5, 13], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 195, 'degree': 192, 'elladic_images': ['8.48.0.60'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.84284347751466123226558081280', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [24487529386319, 183539412225], 'lmfdb_iso': '195.a', 'lmfdb_label': '195.a8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 605, -19750], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '8.48.0-8.q.1.2', '24.96.0-24.be.2.9', '40.96.0-40.bf.1.1', '120.192.1.?', '208.96.0.?', '416.192.2.?', '624.192.1.?', '1040.192.1.?', '1248.384.5.?', '2080.384.5.?', '3120.384.5.?', '6240.768.13.?'], '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': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84284347751466123226558081280', 'prec': 103}, 'szpiro_ratio': 6.317099322920897, '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, 1, -1, 0, 3, 1, -1, 4, -1, 1, 0, 1, -1, 2, -1, -4, -1], 'aplist': [-1, 1, 1, 0, 4, 1, 2, -4, 8, -2, -8, 6, -6, -4, -8, 6, -12, -2, -4, 0, -6, 16, -4, 10, 18], 'class_deg': 16, 'class_size': 8, 'conductor': 195, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '195.a', 'trace_hash': 304833455394853496}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.18531708371704352882074105819', 'prec': 103}, 'conductor': 195, 'gens': [], 'heights': [], 'lmfdb_label': '195.a8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.50285606766124206202283060820', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0057121353224841240456612164052226205', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[62, 476, 1]], 'xcoord_integral_points': [62]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 3], '3': [1, 0], '5': [1, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '195.a8'}
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ec_torsion_growth • Show schema
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id: 7845
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [8]}
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id: 7846
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '195.a8', 'torsion': [8]}
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id: 7844
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 4]}
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id: 7848
{'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 8]}
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id: 7849
{'degree': 4, 'field': [25, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 8]}
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id: 7847
{'degree': 4, 'field': [225, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [4, 4]}
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id: 7853
{'degree': 8, 'field': [-3, 0, -73, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [12]}
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id: 7852
{'degree': 8, 'field': [1, -3, 11, -21, 36, -21, 11, -3, 1], 'lmfdb_label': '195.a8', 'torsion': [16]}
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id: 7850
{'degree': 8, 'field': [625, 0, 0, 0, -25, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [4, 8]}
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id: 7851
{'degree': 8, 'field': [5625, 0, 0, 0, -825, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [16]}
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id: 7855
{'degree': 16, 'field': [1, 0, -13, 0, 67, 0, -247, 0, 640, 0, -247, 0, 67, 0, -13, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 16]}
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id: 7861
{'degree': 16, 'field': [9, 0, -219, 0, 5311, 0, -438, 0, 39, 0, -146, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [24]}
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id: 7859
{'degree': 16, 'field': [4225, 0, 2900, 0, 8200, 0, 5471, 0, 1192, 0, -79, 0, -59, 0, 2, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 12]}
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id: 7860
{'degree': 16, 'field': [38025, 0, -224262, 0, 93025, 0, -4344, 0, 1842, 0, -1730, 0, 240, 0, -24, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [24]}
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id: 7854
{'degree': 16, 'field': [61201, 106680, 1812, -25440, 52708, 4560, -11556, 3360, 645, 960, 144, -120, 58, 0, 12, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [4, 8]}
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id: 7856
{'degree': 16, 'field': [31640625, 0, 0, 0, 4640625, 0, 0, 0, 675000, 0, 0, 0, 825, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 16]}
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id: 7858
{'degree': 16, 'field': [65610000, 0, 0, 0, 2916000, 0, 0, 0, 154225, 0, 0, 0, 360, 0, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 16]}
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id: 7857
{'degree': 16, 'field': [145931659546, 74533928520, 12808253700, -1509512400, -907330774, -307824240, -57700800, -3640320, 2399451, 503160, 69300, 7920, -2014, -240, 0, 0, 1], 'lmfdb_label': '195.a8', 'torsion': [2, 16]}
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ec_localdata • Show schema
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id: 1573
{'conductor': 195, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '195.a8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 1574
{'conductor': 195, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '195.a8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 1575
{'conductor': 195, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '195.a8', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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ec_galrep • Show schema
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id: 1666570
{'adelic_gens': [[1, 0, 32, 1], [4189, 8, 5214, 5957], [1, 32, 0, 1], [25, 16, 2358, 5353], [25, 16, 4504, 5129], [6209, 32, 6208, 33], [5761, 24, 0, 1], [13, 16, 1694, 1305], [1, 32, 4, 129], [3135, 32, 5257, 4065]], 'adelic_image': '6240.768.13.?', 'conductor': 195, 'lmfdb_label': '195.a8', 'prime': 0}
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id: 779
{'conductor': 195, 'elladic_image': '8.48.0.60', 'lmfdb_label': '195.a8', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 195.a does not appear in ec_padic