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ec_curvedata • Show schema
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{'Ciso': '198550cd', 'Clabel': '198550cd2', 'Cnumber': 2, 'abc_quality': 0.9097126155621883, 'absD': 1998542253125000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 456, 'ainvs': [1, 1, 0, -90200, 10609000], 'analytic_rank': 1, 'bad_primes': [2, 5, 11, 19], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 198550, 'degree': 1283040, 'elladic_images': ['8.2.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7209326675543542090721329151', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 13, 'isogeny_degrees': [1, 3], 'jinv': [-575550732865, 14172488], 'lmfdb_iso': '198550.n', 'lmfdb_label': '198550.n1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3608, 84872], 'min_quad_twist_disc': 5, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '8.2.0.a.1', '24.8.0.a.1', '57.8.0-3.a.1.2', '456.16.0.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.5310744699107765651218040323', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 9025], [3, 2, 9025], [5, 14, 7942], [11, 12, 18050], [19, 74, 550]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.15723422940388054933678878764', 'prec': 103}, 'szpiro_ratio': 3.7614075884818954, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, 1, 0, 1, 2, -1, -2, 0, -1, -1, 4, -2, 0, 1, 3, 2, 0, 0], 'aplist': [-1, -1, 0, 2, -1, 4, 3, 0, 6, -6, 4, -8, 6, -4, 12, -12, 15, 8, 4, 0, -7, -8, -15, 9, 19], 'class_deg': 3, 'class_size': 2, 'conductor': 198550, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '198550.n', 'trace_hash': 932577710626263818}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.032004929694036400056929795461', 'prec': 107}, 'conductor': 198550, 'gens': [[10719, 369104, 7]], 'heights': [{'__RealLiteral__': 0, 'data': '5.5310744699107765651218040323', 'prec': 100}], 'lmfdb_label': '198550.n1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.46538400398248059034102652949', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1481471662647071222661909620237808520', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
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lmfdb_label 198550.n1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 8712704
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '198550.n1', 'torsion': [3]}
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id: 8712705
{'degree': 3, 'field': [-88, 32, -1, 1], 'lmfdb_label': '198550.n1', 'torsion': [2]}
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id: 8712708
{'degree': 6, 'field': [-25928, 10996, 1538, 141, 21, -1, 1], 'lmfdb_label': '198550.n1', 'torsion': [6]}
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id: 8712706
{'degree': 6, 'field': [9196, -4712, 1216, -248, 71, -2, 1], 'lmfdb_label': '198550.n1', 'torsion': [2, 2]}
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id: 8712707
{'degree': 6, 'field': [11875, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '198550.n1', 'torsion': [3]}
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id: 8712709
{'degree': 12, 'field': [-19418912, 0, -16964112, 0, 219488, 0, -89528, 0, 2014, 0, -133, 0, 1], 'lmfdb_label': '198550.n1', 'torsion': [4]}
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id: 8712710
{'degree': 12, 'field': [141039376, -71256, -178104, 474950, -178035, -71376, 23891, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '198550.n1', 'torsion': [3, 3]}
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id: 8712711
{'degree': 12, 'field': [585036544, -76315520, 82974408, -13607736, 7537010, -902968, 340013, -34174, 9457, -620, 135, -6, 1], 'lmfdb_label': '198550.n1', 'torsion': [2, 6]}
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id: 8712712
{'degree': 18, 'field': [-80990222024, 18728840856, 16814989902, -3240803603, 25198555098, -16197032310, -1695552538, 4362332877, -657734760, -326965469, 61939041, 12289137, -2180623, -245145, 36897, 2410, -306, -9, 1], 'lmfdb_label': '198550.n1', 'torsion': [9]}
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id: 8712713
{'degree': 18, 'field': [921167317, 0, 0, -2609078, 0, 0, 1222871, 0, 0, 44924, 0, 0, 6387, 0, 0, -102, 0, 0, 1], 'lmfdb_label': '198550.n1', 'torsion': [6]}
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ec_localdata • Show schema
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id: 4915066
{'conductor': 198550, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '198550.n1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 4915067
{'conductor': 198550, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '198550.n1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 4915068
{'conductor': 198550, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '198550.n1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 4915069
{'conductor': 198550, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '198550.n1', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2936428
{'adelic_gens': [[4, 3, 9, 7], [343, 6, 117, 19], [229, 6, 231, 19], [1, 6, 0, 1], [291, 2, 58, 7], [3, 4, 8, 11], [98, 363, 295, 235], [453, 454, 446, 449], [451, 6, 450, 7], [1, 0, 6, 1]], 'adelic_image': '456.16.0.?', 'conductor': 198550, 'lmfdb_label': '198550.n1', 'prime': 0}
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id: 736978
{'conductor': 198550, 'elladic_image': '8.2.0.1', 'lmfdb_label': '198550.n1', 'modell_image': '2G', 'prime': 2}
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id: 736979
{'conductor': 198550, 'elladic_image': '3.4.0.1', 'lmfdb_label': '198550.n1', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 198550.n does not appear in ec_padic