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ec_curvedata • Show schema
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{'Ciso': '5415k', 'Clabel': '5415k2', 'Cnumber': 2, 'abc_quality': 0.9622954410890624, 'absD': 10585323225, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 4560, 'ainvs': [1, 0, 1, -1813, -29437], 'analytic_rank': 0, 'bad_primes': [3, 5, 19], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 5415, 'degree': 3456, 'elladic_images': ['16.48.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.72336832722040378785230115805', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13997521, 225], 'lmfdb_iso': '5415.j', 'lmfdb_label': '5415.j6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5, 2], 'min_quad_twist_disc': -19, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.i.1', '16.48.0.d.2', '24.48.0.bb.2', '40.48.0.bd.1', '48.96.1.n.1', '60.24.0.c.1', '76.24.0.?', '80.192.5.?', '120.96.1.?', '152.48.0.?', '240.384.13.?', '304.96.0.?', '456.96.0.?', '760.96.0.?', '912.192.1.?', '1140.48.0.?', '1520.384.5.?', '2280.192.1.?', '4560.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74885116236281644215221255789', 'prec': 107}, 'szpiro_ratio': 3.9689786913041645, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 1, -1, 1, 1, 0, -3, 1, 1, -4, -1, 2, 0, 1, -1, 2, 1, 0, -1], 'aplist': [1, 1, 1, 0, -4, 2, 2, 0, 0, 2, 0, 10, -10, 4, 8, 10, 4, -2, -12, 8, 10, 0, 12, 6, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 5415, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '5415.j', 'trace_hash': 1563156551168453584}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.23533702238079253702807818759', 'prec': 103}, 'conductor': 5415, 'gens': [], 'heights': [], 'lmfdb_label': '5415.j6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.73240616165107876858566485362', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9296246466043150743426594144591480388', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-27, 13, 1], [49, -25, 1]], 'xcoord_integral_points': [-27, 49]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 0], '3': [1, 0], '5': [1, 0], '19': 'a'}, 'iwp0': 3, 'lmfdb_label': '5415.j6'}
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ec_torsion_growth • Show schema
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id: 281762
{'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 4]}
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id: 281764
{'degree': 4, 'field': [1, 0, -17, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 4]}
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id: 281765
{'degree': 4, 'field': [36, 0, 7, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 8]}
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id: 281763
{'degree': 4, 'field': [510, 30, -29, -2, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 4]}
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id: 281769
{'degree': 8, 'field': [-1557, 522, -1365, 15, -48, -10, -3, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 6]}
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id: 281767
{'degree': 8, 'field': [625, 0, 225, 0, 56, 0, 9, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 8]}
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id: 281768
{'degree': 8, 'field': [2011, -21, 703, -70, 131, -20, 12, -2, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 16]}
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id: 281766
{'degree': 8, 'field': [5185, 430, -284, -290, 141, 2, 4, -4, 1], 'lmfdb_label': '5415.j6', 'torsion': [4, 4]}
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id: 281771
{'degree': 16, 'field': [44100, -239400, -63900, 77400, -490530, 383160, -173250, -8760, 128101, -20100, -24886, 2160, 2076, -60, -76, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 8]}
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id: 281772
{'degree': 16, 'field': [59536, 0, -166712, 0, 226937, 0, -124812, 0, 40268, 0, -7446, 0, 788, 0, -44, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [4, 8]}
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id: 281774
{'degree': 16, 'field': [269361, 0, 389007, 0, 316476, 0, 140119, 0, 36401, 0, 6001, 0, 631, 0, 38, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 12]}
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id: 281773
{'degree': 16, 'field': [390625, 0, 140625, 0, 35000, 0, 6975, 0, 1111, 0, 279, 0, 56, 0, 9, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 16]}
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id: 281770
{'degree': 16, 'field': [2255300100, 0, -2066830200, 0, 745841280, 0, -122238300, 0, 10703941, 0, -513964, 0, 13566, 0, -184, 0, 1], 'lmfdb_label': '5415.j6', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 105547
{'conductor': 5415, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5415.j6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 105548
{'conductor': 5415, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5415.j6', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 105549
{'conductor': 5415, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '5415.j6', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1699243
{'adelic_gens': [[1, 16, 0, 1], [3421, 2888, 2090, 2357], [2639, 0, 0, 4559], [3041, 1216, 2166, 2737], [1, 0, 16, 1], [4545, 16, 4544, 17], [1, 16, 4, 65], [1445, 1216, 1444, 913], [495, 2888, 2128, 2129]], 'adelic_image': '4560.768.13.?', 'conductor': 5415, 'lmfdb_label': '5415.j6', 'prime': 0}
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id: 26754
{'conductor': 5415, 'elladic_image': '16.48.0.3', 'lmfdb_label': '5415.j6', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 5415.j does not appear in ec_padic