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ec_curvedata • Show schema
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{'Ciso': '486720s', 'Clabel': '486720s3', 'Cnumber': 3, 'abc_quality': 1.0847562556631796, 'absD': 104851432982911172972544000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 3120, 'ainvs': [0, 0, 0, -1384233708, 19816551254032], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 486720, 'degree': 264241152, 'elladic_images': ['8.12.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9621459358973783455694279963', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 4], 'jinv': [2543984126301795848, 909361981125], 'lmfdb_iso': '486720.s', 'lmfdb_label': '486720.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -227520, -41682600], 'min_quad_twist_disc': -312, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.o.1', '40.24.0.by.1', '48.24.0-8.o.1.2', '80.48.0.?', '208.24.0.?', '240.96.0.?', '312.24.0.?', '624.48.0.?', '780.12.0.?', '1040.96.3.?', '1560.48.0.?', '3120.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 3, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.4649620591991761069660432001', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 7605], [3, 8, 10816], [5, 6, 97344], [13, 98, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2639311371326234950735215052', 'prec': 100}, 'szpiro_ratio': 5.7087670353475, '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, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 8, 0], 'aplist': [0, 0, -1, -4, 0, 0, -2, 8, -4, 6, 8, 6, -6, 4, 4, 6, -8, 10, 4, 8, 14, 0, -12, -6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 486720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '486720.s', 'trace_hash': 1906316046542900762}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00036184599248183517052213807163', 'prec': 113}, 'conductor': 486720, 'gens': [[-135902, 164845304, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '7.4649620591991761069660432001', 'prec': 100}], 'lmfdb_label': '486720.s1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.058475944109989661797151281602', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.9843312665107897455514837784794246835', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[21788, 0, 1]], 'xcoord_integral_points': [21788]}
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lmfdb_label 486720.s1 does not appear in ec_iwasawa
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lmfdb_label 486720.s1 does not appear in ec_torsion_growth
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ec_localdata • Show schema
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id: 11997257
{'conductor': 486720, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '486720.s1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 11997258
{'conductor': 486720, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '486720.s1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 11997259
{'conductor': 486720, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '486720.s1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 11997260
{'conductor': 486720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '486720.s1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 4647669
{'adelic_gens': [[1039, 0, 0, 3119], [1, 16, 0, 1], [15, 166, 2834, 3075], [1, 8, 8, 65], [1286, 2337, 3027, 2060], [479, 2064, 1752, 911], [1678, 3, 1341, 1060], [1, 0, 16, 1], [2333, 2850, 768, 2267], [3105, 16, 3104, 17]], 'adelic_image': '3120.192.3.?', 'conductor': 486720, 'lmfdb_label': '486720.s1', 'prime': 0}
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id: 1612011
{'conductor': 486720, 'elladic_image': '8.12.0.10', 'lmfdb_label': '486720.s1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 486720.s does not appear in ec_padic