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ec_curvedata • Show schema
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{'Ciso': '27584i', 'Clabel': '27584i1', 'Cnumber': 1, 'abc_quality': 0.9455399461306241, 'absD': 118472377892864, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 17240, 'ainvs': [0, 1, 0, -157441, 23998303], 'analytic_rank': 0, 'bad_primes': [2, 431], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 27584, 'degree': 122880, 'elladic_images': ['5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6829504622871631520170890021', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 5], 'jinv': [-1646417855125441, 451936256], 'lmfdb_iso': '27584.s', 'lmfdb_label': '27584.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -2460, 45949], 'min_quad_twist_disc': 8, 'modell_images': ['5B.4.1'], 'modm_images': ['5.12.0.a.1', '40.24.0-5.a.1.3', '862.2.0.?', '4310.24.1.?', '17240.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.64322969144724518789124081991', 'prec': 103}, 'szpiro_ratio': 4.646899052305992, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, -1, 0, -2, 0, -2, 0, 3, 0, 6, 0, -1, 0, -2, 0, 5, 0], 'aplist': [0, 1, -1, -2, 3, 6, -2, 5, 9, -5, -8, -8, 2, 6, -2, 1, 15, -2, 2, 2, 14, 0, 16, 10, 3], 'class_deg': 5, 'class_size': 2, 'conductor': 27584, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '27584.s', 'trace_hash': 1330477683910611754}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.034530892370524783437229960865', 'prec': 107}, 'conductor': 27584, 'gens': [], 'heights': [], 'lmfdb_label': '27584.s1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.57630857255770381118973433687', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3052342902308152447589373474597843197', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0], '431': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '27584.s1'}
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ec_torsion_growth • Show schema
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id: 1379857
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '27584.s1', 'torsion': [5]}
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id: 1379858
{'degree': 3, 'field': [-8, -1, 0, 1], 'lmfdb_label': '27584.s1', 'torsion': [2]}
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id: 1379860
{'degree': 6, 'field': [62, -80, 13, -16, -8, 0, 1], 'lmfdb_label': '27584.s1', 'torsion': [10]}
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id: 1379859
{'degree': 6, 'field': [164, -208, 123, -14, 0, -2, 1], 'lmfdb_label': '27584.s1', 'torsion': [2, 2]}
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id: 1379861
{'degree': 8, 'field': [-108, 0, 110, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '27584.s1', 'torsion': [3]}
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id: 1379862
{'degree': 12, 'field': [-110336, 0, -208384, 0, 78652, 0, -11840, 0, 413, 0, 0, 0, 1], 'lmfdb_label': '27584.s1', 'torsion': [4]}
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id: 1379863
{'degree': 12, 'field': [55652, -14032, 37380, -39056, 28017, -11580, 3100, -1068, 322, 12, -8, -4, 1], 'lmfdb_label': '27584.s1', 'torsion': [2, 10]}
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id: 1379864
{'degree': 16, 'field': [256, 0, 3104, 0, 3076, 0, -60624, 0, 12816, 0, -516, 0, 40, 0, -16, 0, 1], 'lmfdb_label': '27584.s1', 'torsion': [15]}
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id: 1379865
{'degree': 20, 'field': [11348632766042996, -29954593843479616, 37079745017171738, -28482252800040344, 15123971450539457, -5844205417434532, 1680040920507184, -358819341036292, 55075450431166, -5416770299348, 172600440514, 38707015228, -6528339174, 350282392, 16624724, -3323188, 111667, 8224, -632, -4, 1], 'lmfdb_label': '27584.s1', 'torsion': [5]}
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ec_localdata • Show schema
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id: 636403
{'conductor': 27584, 'conductor_valuation': 6, 'discriminant_valuation': 38, 'j_denominator_valuation': 20, 'kodaira_symbol': -32, 'lmfdb_label': '27584.s1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 636404
{'conductor': 27584, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27584.s1', 'prime': 431, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1847851
{'adelic_gens': [[6, 13, 17185, 17121], [4311, 0, 0, 1], [15474, 17235, 12965, 12934], [1, 0, 10, 1], [17239, 17230, 0, 14653], [8619, 0, 0, 17239], [6, 13, 4255, 4191], [4301, 10, 4300, 11], [17231, 10, 17230, 11], [1, 10, 0, 1]], 'adelic_image': '17240.48.1.?', 'conductor': 27584, 'lmfdb_label': '27584.s1', 'prime': 0}
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id: 124726
{'conductor': 27584, 'elladic_image': '5.12.0.1', 'lmfdb_label': '27584.s1', 'modell_image': '5B.4.1', 'prime': 5}
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lmfdb_iso 27584.s does not appear in ec_padic