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ec_curvedata • Show schema
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{'Ciso': '278784bg', 'Clabel': '278784bg1', 'Cnumber': 1, 'abc_quality': 1.2424379096229237, 'absD': 53559759610368, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 264, 'ainvs': [0, 0, 0, -3630, 362032], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 278784, 'degree': 655360, 'elladic_images': ['8.24.0.80'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3165393563501350851086788112', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2], 'jinv': [-8000, 81], 'lmfdb_iso': '278784.bg', 'lmfdb_label': '278784.bg2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -13, 85], 'min_quad_twist_disc': 264, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.f.1', '8.24.0.n.1', '24.48.1.cm.1', '88.48.0.?', '264.96.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, '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': '-0.95157480980306401468283968734', 'prec': 107}, 'szpiro_ratio': 3.1202361182959457, '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, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, 0, 4, 0, 4, -2, -4, 8, 8, -4, 4, 6, 4, 8, -8, -12, 12, -12, -8, 6, 4, 4, 6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 278784, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '278784.bg', 'trace_hash': 391380585401727483}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.071856894608204936986815632749', 'prec': 107}, 'conductor': 278784, 'gens': [], 'heights': [], 'lmfdb_label': '278784.bg2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.53737740974741696976060263520', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2990192779793357580848210816350958194', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-88, 0, 1]], 'xcoord_integral_points': [-88]}
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lmfdb_label 278784.bg2 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 11877385
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [2, 2]}
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id: 11877386
{'degree': 4, 'field': [-2178, 0, 0, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [4]}
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id: 11877387
{'degree': 4, 'field': [2178, 0, 0, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [2, 4]}
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id: 11877389
{'degree': 8, 'field': [-702768, 0, 127776, 0, 0, 0, -88, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [6]}
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id: 11877388
{'degree': 8, 'field': [1185921, 0, -143748, 0, 8712, 0, -132, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [4, 4]}
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id: 11877391
{'degree': 16, 'field': [94582, -278160, 329704, -341832, 304736, -170328, 131604, -58608, 29453, -9840, 4104, -912, 398, -48, 28, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [2, 8]}
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id: 11877392
{'degree': 16, 'field': [1068114, -1470384, 621592, 100984, -129612, -65424, 53404, 13232, -5255, -4264, -136, 576, 158, -32, -20, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [2, 8]}
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id: 11877390
{'degree': 16, 'field': [6853284, -1172736, -4781664, 969792, 343168, -620256, 151024, -59792, -16860, 21120, -6896, 2496, -464, -16, 24, -8, 1], 'lmfdb_label': '278784.bg2', 'torsion': [8]}
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id: 11877393
{'degree': 16, 'field': [151659225, 0, 2249936888, 0, 399549424, 0, 14391816, 0, -542038, 0, -5096, 0, 2928, 0, 104, 0, 1], 'lmfdb_label': '278784.bg2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 6905634
{'conductor': 278784, 'conductor_valuation': 8, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '278784.bg2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 6905635
{'conductor': 278784, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '278784.bg2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 6905636
{'conductor': 278784, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '278784.bg2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 3423478
{'adelic_gens': [[1, 0, 8, 1], [119, 0, 0, 263], [1, 8, 0, 1], [1, 4, 4, 17], [257, 8, 256, 9], [175, 88, 220, 87], [34, 143, 121, 210], [98, 253, 33, 98], [3, 8, 256, 243]], 'adelic_image': '264.96.1.?', 'conductor': 278784, 'lmfdb_label': '278784.bg2', 'prime': 0}
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id: 992642
{'conductor': 278784, 'elladic_image': '8.24.0.80', 'lmfdb_label': '278784.bg2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 278784.bg does not appear in ec_padic