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ec_curvedata • Show schema
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{'Ciso': '9408cd', 'Clabel': '9408cd4', 'Cnumber': 4, 'abc_quality': 1.0015974661127929, 'absD': 1416433663475712, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [0, -1, 0, -122369, 16417185], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 9408, 'degree': 49152, 'elladic_images': ['8.48.0.220'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7403076384785417327281743479', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6570725617, 45927], 'lmfdb_iso': '9408.m', 'lmfdb_label': '9408.m3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -39, 90], 'min_quad_twist_disc': 56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0-8.bb.1.2', '28.12.0.h.1', '48.96.0-48.bf.1.2', '56.96.0-56.bl.2.8', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7178992968149188558124724386', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020601', 'prec': 107}, 'szpiro_ratio': 5.110546180448468, '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, -2, 0, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 6, 0, -4, 0], 'aplist': [0, -1, -2, 0, 4, -2, 6, -4, 0, 2, 0, -6, -2, -4, 0, -6, -12, -2, 4, 0, 6, 16, 12, 14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 9408, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '9408.m', 'trace_hash': 1298151834783419293}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.030788461772754535022719902396', 'prec': 107}, 'conductor': 9408, 'gens': [[187, 196, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7178992968149188558124724386', 'prec': 100}], 'lmfdb_label': '9408.m3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48226265395982068031940353104', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3139146964706899566918711216866091866', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[215, 0, 1]], 'xcoord_integral_points': [-352, 187, 215]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '9408.m3'}
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ec_torsion_growth • Show schema
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id: 490092
{'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [8]}
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id: 490091
{'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [2, 2]}
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id: 490093
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [4]}
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id: 490094
{'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [2, 8]}
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id: 490098
{'degree': 8, 'field': [-2352, 0, 1288, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [6]}
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id: 490095
{'degree': 8, 'field': [1, 0, 4, 0, -1, 0, 4, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [2, 4]}
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id: 490096
{'degree': 8, 'field': [4, 0, 10, 0, 5, 0, -2, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [8]}
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id: 490097
{'degree': 8, 'field': [441, 0, -168, 0, 67, 0, -10, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [16]}
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id: 490101
{'degree': 16, 'field': [1, 0, -28, 0, 242, 0, -840, 0, 1259, 0, -840, 0, 242, 0, -28, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [2, 16]}
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id: 490099
{'degree': 16, 'field': [16, 0, 0, 0, -24, 0, 0, 0, 73, 0, 0, 0, 15, 0, 0, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [4, 8]}
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id: 490100
{'degree': 16, 'field': [81, 0, 180, 0, 130, 0, 384, 0, 651, 0, 320, 0, 114, 0, 12, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [2, 16]}
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id: 490104
{'degree': 16, 'field': [529, 0, -5812, 0, 973, 0, -6160, 0, 5026, 0, -1456, 0, 196, 0, -16, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [12]}
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id: 490102
{'degree': 16, 'field': [19881, 0, 6816, 0, -6767, 0, 1140, 0, -2166, 0, -16, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [2, 6]}
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id: 490103
{'degree': 16, 'field': [3073009, 0, -10127818, 0, 3153397, 0, -555312, 0, 70926, 0, -6582, 0, 520, 0, -28, 0, 1], 'lmfdb_label': '9408.m3', 'torsion': [24]}
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ec_localdata • Show schema
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id: 198040
{'conductor': 9408, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '9408.m3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 198041
{'conductor': 9408, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '9408.m3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 198042
{'conductor': 9408, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '9408.m3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1726265
{'adelic_gens': [[5, 4, 332, 333], [1, 16, 0, 1], [15, 2, 238, 323], [335, 320, 244, 123], [118, 73, 293, 282], [321, 16, 320, 17], [1, 0, 16, 1], [113, 16, 232, 129], [88, 335, 113, 326]], 'adelic_image': '336.192.1.?', 'conductor': 9408, 'lmfdb_label': '9408.m3', 'prime': 0}
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id: 45721
{'conductor': 9408, 'elladic_image': '8.48.0.220', 'lmfdb_label': '9408.m3', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 394580
{'lmfdb_iso': '9408.m', 'p': 5, 'prec': 20, 'unit': 17143344979599, 'val': 1}
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id: 394586
{'lmfdb_iso': '9408.m', 'p': 11, 'prec': 20, 'unit': 13708324182751673793, 'val': 1}
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id: 394584
{'lmfdb_iso': '9408.m', 'p': 13, 'prec': 20, 'unit': 1326217199314572996036, 'val': 1}
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id: 394587
{'lmfdb_iso': '9408.m', 'p': 17, 'prec': 20, 'unit': 13920675402641437783733, 'val': 1}
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id: 394588
{'lmfdb_iso': '9408.m', 'p': 19, 'prec': 20, 'unit': 751436606497046039368422, 'val': 1}
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id: 394583
{'lmfdb_iso': '9408.m', 'p': 29, 'prec': 20, 'unit': 1966021324288636773467569449, 'val': 1}
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id: 394594
{'lmfdb_iso': '9408.m', 'p': 37, 'prec': 20, 'unit': 484727390636375636094644111236, 'val': 1}
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id: 394581
{'lmfdb_iso': '9408.m', 'p': 41, 'prec': 20, 'unit': 12193492290250488130308080169, 'val': 2}
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id: 394582
{'lmfdb_iso': '9408.m', 'p': 43, 'prec': 20, 'unit': 9644511421267068375655609682498, 'val': 1}
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id: 394589
{'lmfdb_iso': '9408.m', 'p': 53, 'prec': 20, 'unit': 245569830191478348340344143148322, 'val': 1}
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id: 394592
{'lmfdb_iso': '9408.m', 'p': 59, 'prec': 20, 'unit': 3349210376896645758309494340606051, 'val': 1}
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id: 394593
{'lmfdb_iso': '9408.m', 'p': 61, 'prec': 20, 'unit': 4131695783836036247748937203371219, 'val': 1}
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id: 394579
{'lmfdb_iso': '9408.m', 'p': 67, 'prec': 20, 'unit': 41417902693081330758740381735843564, 'val': 1}
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id: 394590
{'lmfdb_iso': '9408.m', 'p': 73, 'prec': 20, 'unit': 164500874372426971523097603704609832, 'val': 1}
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id: 394585
{'lmfdb_iso': '9408.m', 'p': 79, 'prec': 20, 'unit': 137672294181417100625613336157886094, 'val': 1}
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id: 394578
{'lmfdb_iso': '9408.m', 'p': 83, 'prec': 20, 'unit': 261413784405790775811811351421922169, 'val': 1}
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id: 394591
{'lmfdb_iso': '9408.m', 'p': 89, 'prec': 20, 'unit': 1360408023984014256203639218192085884, 'val': 1}
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id: 394577
{'lmfdb_iso': '9408.m', 'p': 97, 'prec': 20, 'unit': 44552286487271835999712174232816217273, 'val': 1}