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ec_curvedata • Show schema
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{'Ciso': '4080bb', 'Clabel': '4080bb3', 'Cnumber': 3, 'abc_quality': 1.0024850789671809, 'absD': 1958400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 136, 'ainvs': [0, 1, 0, -104656, 12996500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4080, 'degree': 18432, 'elladic_images': ['8.24.0.104'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4936800942707950099213284315', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 4], 'jinv': [30949975477232209, 478125000], 'lmfdb_iso': '4080.x', 'lmfdb_label': '4080.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -6541, -206341], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.m.1.7', '68.12.0-4.c.1.2', '136.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80053291371084970050409631004', 'prec': 103}, 'szpiro_ratio': 5.56768550602491, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, -1, 0, 4, 0, 1, 0, 4, 0, -2, 0, -1, 0, 1, 0, 4, 0], 'aplist': [0, 1, -1, 4, 4, -2, 1, 4, 4, 2, -4, -6, 2, 12, -8, -2, -12, 2, -4, 4, -14, 12, 4, 10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 4080, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4080.x', 'trace_hash': 889235604775964580}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.050420361446180132661560950949', 'prec': 107}, 'conductor': 4080, 'gens': [], 'heights': [], 'lmfdb_label': '4080.x1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.75981413314468570676668003095', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0392565325787428270667201237982870798', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[187, 0, 1]], 'xcoord_integral_points': [187]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0], '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4080.x1'}
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ec_torsion_growth • Show schema
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id: 214226
{'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [2, 2]}
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id: 214227
{'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '4080.x1', 'torsion': [4]}
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id: 214228
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [4]}
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id: 214229
{'degree': 4, 'field': [2, 12, -11, -2, 1], 'lmfdb_label': '4080.x1', 'torsion': [2, 4]}
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id: 214230
{'degree': 4, 'field': [256, 52, -40, -1, 1], 'lmfdb_label': '4080.x1', 'torsion': [8]}
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id: 214233
{'degree': 8, 'field': [-288, 576, 48, -576, 178, 104, -37, -2, 1], 'lmfdb_label': '4080.x1', 'torsion': [2, 8]}
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id: 214234
{'degree': 8, 'field': [-48, 0, 89, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [6]}
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id: 214232
{'degree': 8, 'field': [289, 0, -340, 0, 104, 0, -4, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [8]}
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id: 214231
{'degree': 8, 'field': [91204, 0, 7376, 0, -588, 0, 8, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [2, 4]}
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id: 214236
{'degree': 16, 'field': [16, 0, 96, 0, 288, 0, -24, 0, 1, 0, 12, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [2, 8]}
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id: 214240
{'degree': 16, 'field': [2500, 0, -2500, 0, 625, 0, -36768, 0, 9492, 0, -462, 0, 64, 0, -16, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [12]}
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id: 214239
{'degree': 16, 'field': [83648, -158768, 196906, 129846, -537587, 451688, 30694, -134072, 9558, 12094, 1022, -1336, -202, 168, -4, -8, 1], 'lmfdb_label': '4080.x1', 'torsion': [12]}
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id: 214237
{'degree': 16, 'field': [23970816, 0, -278660736, 0, 644402952, 0, -244389960, 0, 34396236, 0, -1597320, 0, 32742, 0, -306, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [16]}
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id: 214238
{'degree': 16, 'field': [469805625, 0, -144501156, 0, -49366980, 0, 89012, 0, 115022, 0, -26860, 0, 2380, 0, -68, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [2, 6]}
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id: 214235
{'degree': 16, 'field': [547981281, 0, 0, 0, 0, 0, 0, 0, 795906, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '4080.x1', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 76910
{'conductor': 4080, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '4080.x1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 76911
{'conductor': 4080, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4080.x1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 76912
{'conductor': 4080, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '4080.x1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 76913
{'conductor': 4080, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4080.x1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1690653
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [120, 59, 89, 118], [13, 16, 62, 11], [1, 4, 4, 17], [129, 8, 128, 9], [12, 1, 103, 6], [7, 6, 130, 131]], 'adelic_image': '136.48.0.?', 'conductor': 4080, 'lmfdb_label': '4080.x1', 'prime': 0}
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id: 20469
{'conductor': 4080, 'elladic_image': '8.24.0.104', 'lmfdb_label': '4080.x1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 4080.x does not appear in ec_padic