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ec_curvedata • Show schema
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{'Ciso': '91091f', 'Clabel': '91091f1', 'Cnumber': 1, 'abc_quality': 0.8254556483942886, 'absD': 6246561772451, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 50050, 'ainvs': [0, 1, 1, -2760, -133493], 'analytic_rank': 0, 'bad_primes': [7, 11, 13], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 91091, 'degree': 155520, 'elladic_images': ['25.60.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1427009559229717685900261644', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 5, 25], 'jinv': [-4096, 11], 'lmfdb_iso': '91091.s', 'lmfdb_label': '91091.s3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, 0, 0], 'min_quad_twist_disc': -91, 'modell_images': ['5B.4.1'], 'modm_images': ['5.12.0.a.1', '22.2.0.a.1', '25.60.0.a.1', '110.24.1.?', '275.300.12.?', '455.24.0.?', '550.600.37.?', '2275.120.0.?', '10010.48.1.?', '25025.600.12.?', '50050.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[7, 26, 1859], [11, 12, 8281], [13, 86, 539]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1127287973354532519893939281', 'prec': 103}, 'szpiro_ratio': 3.2499274626848296, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 2, 1, 2, 1, 2, 0, 0, -2, 2, -1, 2, 0, 0, 1, -4, 2, -4, 0, 2], 'aplist': [2, 1, 1, 0, -1, 0, 2, 0, -1, 0, 7, -3, -8, -6, 8, -6, 5, -12, 7, 3, 4, -10, -6, 15, -7], 'class_deg': 25, 'class_size': 3, 'conductor': 91091, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '91091.s', 'trace_hash': 1367254378167536447}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.10173316612395380866527509406', 'prec': 103}, 'conductor': 91091, 'gens': [], 'heights': [], 'lmfdb_label': '91091.s3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.30585106781891833990203797675', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.8936170851026934384326076280376581707', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [6, 7, 0], '3': [2, 0], '5': [2, 0], '7': 'a', '11': [0, 0], '13': 'a', '17': [0, 0], '19': [0, 0, 0], '23': [0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '91091.s3'}
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ec_torsion_growth • Show schema
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id: 4253237
{'degree': 2, 'field': [23, -1, 1], 'lmfdb_label': '91091.s3', 'torsion': [5]}
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id: 4253238
{'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '91091.s3', 'torsion': [2]}
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id: 4253239
{'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '91091.s3', 'torsion': [2, 2]}
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id: 4253240
{'degree': 6, 'field': [11111, -349, 1566, -49, 70, -1, 1], 'lmfdb_label': '91091.s3', 'torsion': [10]}
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id: 4253241
{'degree': 8, 'field': [-1073869, -364276, -202747, 11871, -3309, 210, -2, -2, 1], 'lmfdb_label': '91091.s3', 'torsion': [3]}
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id: 4253242
{'degree': 10, 'field': [8914201, -911909, 1619869, -142113, 124700, -8780, 5070, -256, 109, -3, 1], 'lmfdb_label': '91091.s3', 'torsion': [25]}
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id: 4253243
{'degree': 12, 'field': [-23963676266, 1268719560, 868930068, 121466316, 63131404, 2048924, 594420, 53740, -13350, 178, 6, -2, 1], 'lmfdb_label': '91091.s3', 'torsion': [4]}
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id: 4253244
{'degree': 12, 'field': [125228492, -26268716, 37099492, -5790856, 4366606, -505722, 264033, -21892, 8677, -470, 147, -4, 1], 'lmfdb_label': '91091.s3', 'torsion': [2, 10]}
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id: 4253245
{'degree': 16, 'field': [72513334089, 0, 25152653232, 0, 3857207736, 0, 339572485, 0, 18706184, 0, 659131, 0, 14497, 0, 182, 0, 1], 'lmfdb_label': '91091.s3', 'torsion': [15]}
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id: 4253246
{'degree': 20, 'field': [159551406436304255, -12238943880474995, -31004744638639335, 1567797254230125, 2749586789557816, -81145128257457, -144573130644990, 1988183456700, 4951324493175, -12819274896, -114942929138, -564317875, 1825268195, 16802800, -19551033, -205999, 135420, 1240, -550, -3, 1], 'lmfdb_label': '91091.s3', 'torsion': [5]}
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ec_localdata • Show schema
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id: 2227380
{'conductor': 91091, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '91091.s3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 2227381
{'conductor': 91091, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '91091.s3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 2227382
{'conductor': 91091, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '91091.s3', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2263557
{'adelic_gens': [[1, 0, 50, 1], [35491, 20930, 25935, 23661], [19566, 13195, 36127, 36037], [23099, 0, 0, 50049], [1, 50, 0, 1], [28599, 0, 0, 50049], [38, 41, 47491, 47289], [50001, 50, 50000, 51]], 'adelic_image': '50050.1200.37.?', 'conductor': 91091, 'lmfdb_label': '91091.s3', 'prime': 0}
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id: 369236
{'conductor': 91091, 'elladic_image': '25.60.0.1', 'lmfdb_label': '91091.s3', 'modell_image': '5B.4.1', 'prime': 5}
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lmfdb_iso 91091.s does not appear in ec_padic