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ec_curvedata • Show schema
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{'Ciso': '8280k', 'Clabel': '8280k1', 'Cnumber': 1, 'abc_quality': 1.0003317584064302, 'absD': 115482299361120000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 552, 'ainvs': [0, 0, 0, -35607, 16553194], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8280, 'degree': 49152, 'elladic_images': ['8.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9547302142888981767732063597', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [-26752376766544, 618796614375], 'lmfdb_iso': '8280.r', 'lmfdb_label': '8280.r4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -3956, -614400], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.p.1', '12.12.0-4.c.1.2', '24.24.0-8.p.1.8', '46.6.0.a.1', '92.12.0.?', '184.24.0.?', '276.24.0.?', '552.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.94332594958154645813076232693', 'prec': 103}, 'szpiro_ratio': 5.183929002314052, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0], 'aplist': [0, 0, 1, 0, 0, -2, 6, 0, 1, -6, 0, -6, 6, 0, 8, 6, 12, 10, 0, 0, -6, 8, 0, -10, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 8280, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '8280.r', 'trace_hash': 715867513851552401}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.020051317261137187571777369099', 'prec': 107}, 'conductor': 8280, 'gens': [], 'heights': [], 'lmfdb_label': '8280.r4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27888572273083059912890674745', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2310857818466447930312539795696806271', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-301, 0, 1]], 'xcoord_integral_points': [-301]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '23': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '8280.r4'}
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ec_torsion_growth • Show schema
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id: 433237
{'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '8280.r4', 'torsion': [4]}
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id: 433238
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '8280.r4', 'torsion': [4]}
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id: 433236
{'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '8280.r4', 'torsion': [2, 2]}
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id: 433239
{'degree': 4, 'field': [36, -6, -5, -1, 1], 'lmfdb_label': '8280.r4', 'torsion': [2, 4]}
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id: 433243
{'degree': 8, 'field': [-29403, 0, -1512, 0, 594, 0, 0, 0, 1], 'lmfdb_label': '8280.r4', 'torsion': [6]}
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id: 433240
{'degree': 8, 'field': [36, 12, 70, 114, 77, 2, 4, -4, 1], 'lmfdb_label': '8280.r4', 'torsion': [2, 4]}
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id: 433242
{'degree': 8, 'field': [49, -56, 36, -32, 23, -16, 4, 0, 1], 'lmfdb_label': '8280.r4', 'torsion': [8]}
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id: 433241
{'degree': 8, 'field': [225, 0, -5016, 0, 370, 0, 40, 0, 1], 'lmfdb_label': '8280.r4', 'torsion': [8]}
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id: 433244
{'degree': 16, 'field': [1296, -432, 72, -1320, 328, -396, 786, -254, 233, -278, 200, -86, 27, -12, 8, -4, 1], 'lmfdb_label': '8280.r4', 'torsion': [4, 4]}
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id: 433246
{'degree': 16, 'field': [3844, 4712, -2532, -1720, 8242, 7184, 3934, 2824, 807, -152, 206, 104, -35, -8, -2, 0, 1], 'lmfdb_label': '8280.r4', 'torsion': [2, 8]}
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id: 433249
{'degree': 16, 'field': [131769, 0, 20328, 0, 27094, 0, -3696, 0, 4719, 0, 112, 0, -66, 0, 0, 0, 1], 'lmfdb_label': '8280.r4', 'torsion': [12]}
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id: 433245
{'degree': 16, 'field': [37015056, 0, -9612720, 0, 908476, 0, -266364, 0, 43077, 0, 28, 0, -117, 0, -12, 0, 1], 'lmfdb_label': '8280.r4', 'torsion': [2, 8]}
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id: 433248
{'degree': 16, 'field': [59497965, -93818070, -104567760, 10797756, 10974198, 9763560, 4740160, 2209826, 809385, -20622, 20814, 2094, -966, 114, 24, -4, 1], 'lmfdb_label': '8280.r4', 'torsion': [12]}
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id: 433247
{'degree': 16, 'field': [467738064, -1837800576, 1707992352, 248476032, -96463656, -33111720, 10668492, 321576, -71483, -30896, 31840, -14912, 3274, -392, 76, -8, 1], 'lmfdb_label': '8280.r4', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 172287
{'conductor': 8280, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '8280.r4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 172288
{'conductor': 8280, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '8280.r4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 172289
{'conductor': 8280, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '8280.r4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 172290
{'conductor': 8280, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8280.r4', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1718753
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [307, 486, 258, 163], [388, 369, 207, 190], [7, 6, 546, 547], [169, 348, 534, 439], [367, 0, 0, 551], [545, 8, 544, 9]], 'adelic_image': '552.48.0.?', 'conductor': 8280, 'lmfdb_label': '8280.r4', 'prime': 0}
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id: 40599
{'conductor': 8280, 'elladic_image': '8.12.0.9', 'lmfdb_label': '8280.r4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 8280.r does not appear in ec_padic