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ec_curvedata • Show schema
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{'Ciso': '80586l', 'Clabel': '80586l1', 'Cnumber': 1, 'abc_quality': 0.9869944369461394, 'absD': 301854042633377482915392, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [1, -1, 0, -40233672, 94613889024], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 80586, 'degree': 12165120, 'elladic_images': ['8.6.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2701460885335135401736881892', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [5577108481460841625, 233729407061568], 'lmfdb_iso': '80586.k', 'lmfdb_label': '80586.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -36946, 2629412], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.d.1', '66.6.0.a.1', '264.12.0.?'], '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, 'serre_invariants': [[2, 4, 1089], [3, 8, 4477], [11, 72, 666], [37, 38, 2178]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5218923078002734224450937818', 'prec': 100}, 'szpiro_ratio': 5.677949192558976, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, 1, 0, 0, 2, -1, 0, 0, 0, 0, -4, -2, 0, 1, 2, 0, 8, 0], 'aplist': [-1, 0, 0, 2, 0, -4, 2, 8, 2, -2, -8, 1, 6, -12, 10, -12, 4, 0, -12, 14, 14, 10, 12, -6, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 80586, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '80586.k', 'trace_hash': 1058404827406040622}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0014440665142576822337015247622', 'prec': 110}, 'conductor': 80586, 'gens': [], 'heights': [], 'lmfdb_label': '80586.k1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.096110940326808353703246851102', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5377750452289336592519496176371299540', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[3072, -1536, 1]], 'xcoord_integral_points': [3072]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 0], '3': 'a', '11': 'a', '37': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '80586.k1'}
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ec_torsion_growth • Show schema
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id: 3790638
{'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 2]}
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id: 3790639
{'degree': 4, 'field': [1, -2, 5, -2, 1], 'lmfdb_label': '80586.k1', 'torsion': [4]}
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id: 3790642
{'degree': 8, 'field': [-120240, 10194, 2091, -2943, -108, 153, -12, -1, 1], 'lmfdb_label': '80586.k1', 'torsion': [6]}
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id: 3790641
{'degree': 8, 'field': [4, 0, -79, 0, -45, 0, 23, 0, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 4]}
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id: 3790640
{'degree': 8, 'field': [187, 88, -40, -92, 37, 8, 2, -4, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 4]}
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id: 3790644
{'degree': 16, 'field': [63872064, 0, -7622592, 0, 679024, 0, -1342113, 0, 269946, 0, -30017, 0, 1977, 0, -66, 0, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 6]}
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id: 3790643
{'degree': 16, 'field': [50598787776, -95752521984, 87590924800, -29262057152, 8180424072, 409364896, -4836424, 45543192, -112247, 956284, 47230, -4704, 855, -560, 66, -4, 1], 'lmfdb_label': '80586.k1', 'torsion': [8]}
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ec_localdata • Show schema
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id: 1960162
{'conductor': 80586, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '80586.k1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1960163
{'conductor': 80586, 'conductor_valuation': 2, 'discriminant_valuation': 17, 'j_denominator_valuation': 11, 'kodaira_symbol': -15, 'lmfdb_label': '80586.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 1960164
{'conductor': 80586, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '80586.k1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1960165
{'conductor': 80586, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '80586.k1', 'prime': 37, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2195177
{'adelic_gens': [[178, 1, 175, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [26, 1, 119, 0], [261, 4, 260, 5], [169, 100, 32, 231], [133, 4, 2, 9]], 'adelic_image': '264.12.0.?', 'conductor': 80586, 'lmfdb_label': '80586.k1', 'prime': 0}
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id: 330645
{'conductor': 80586, 'elladic_image': '8.6.0.4', 'lmfdb_label': '80586.k1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 80586.k does not appear in ec_padic