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ec_curvedata • Show schema
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{'Ciso': '221760iq', 'Clabel': '221760iq4', 'Cnumber': 4, 'abc_quality': 0.9976896458230765, 'absD': 145457571691254003793920, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 18480, 'ainvs': [0, 0, 0, -14656332, -11388908176], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 221760, 'degree': 15728640, 'elladic_images': ['16.24.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1415903061107395158246298326', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 302, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1821931919215868881, 761147600816295], 'lmfdb_iso': '221760.lq', 'lmfdb_label': '221760.lq4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -25445, 821730], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.4', '24.24.0-8.n.1.9', '48.48.0-48.e.1.27', '56.24.0.bu.2', '112.48.0.?', '168.48.0.?', '220.12.0.?', '336.96.0.?', '440.24.0.?', '880.48.0.?', '1320.48.0.?', '2640.96.0.?', '3080.48.0.?', '6160.96.0.?', '9240.96.0.?', '18480.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, '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': '1.5525633909367667060011590320', 'prec': 100}, 'szpiro_ratio': 4.964904495213676, '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, 1, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, 1, 1, -1, 2, -2, -4, 0, 6, 0, -6, 6, 4, 0, -2, 4, -6, -12, 0, 10, 8, -4, -10, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 221760, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '221760.lq', 'trace_hash': 1054270386529174261}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0018674514992939639449290098775', 'prec': 110}, 'conductor': 221760, 'gens': [], 'heights': [], 'lmfdb_label': '221760.lq4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.080075908750647746156038832640', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5624290800207278769932426444728818022', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-3356, 0, 1]], 'xcoord_integral_points': [-3356]}
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lmfdb_label 221760.lq4 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 9649171
{'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [2, 2]}
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id: 9649173
{'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [4]}
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id: 9649172
{'degree': 2, 'field': [330, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [4]}
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id: 9649175
{'degree': 4, 'field': [81, 0, 24, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [8]}
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id: 9649174
{'degree': 4, 'field': [3721, 0, -98, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [2, 4]}
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id: 9649176
{'degree': 4, 'field': [10410, 180, -179, -2, 1], 'lmfdb_label': '221760.lq4', 'torsion': [8]}
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id: 9649180
{'degree': 8, 'field': [-52272, 0, 0, 0, 792, 0, 46, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [6]}
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id: 9649178
{'degree': 8, 'field': [256, 0, 234, 0, 41, 0, -6, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [8]}
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id: 9649179
{'degree': 8, 'field': [133956, 0, -4668, 0, 1093, 0, -38, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [2, 8]}
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id: 9649177
{'degree': 8, 'field': [148996, 0, -64764, 0, 1381, 0, -84, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [2, 4]}
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id: 9649182
{'degree': 16, 'field': [276676, 0, -74920, 0, 76016, 0, -6540, 0, 6221, 0, 240, 0, 206, 0, 20, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [2, 8]}
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id: 9649187
{'degree': 16, 'field': [984753, -2256156, 4910976, -6425790, 6164982, -4009398, 2157955, -794096, 318558, -92218, 31373, -8004, 2153, -406, 78, -8, 1], 'lmfdb_label': '221760.lq4', 'torsion': [12]}
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id: 9649183
{'degree': 16, 'field': [8434034569, 0, 1137096508, 0, 313365650, 0, 54328572, 0, 7601747, 0, 462996, 0, 13334, 0, 184, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [16]}
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id: 9649184
{'degree': 16, 'field': [14403600225, 0, 511183319850, 0, 196254274405, 0, 20964184290, 0, 912520176, 0, 18313816, 0, 170001, 0, 696, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [16]}
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id: 9649185
{'degree': 16, 'field': [45546815889, 0, -15535305972, 0, -16865609085, 0, -4324632084, 0, -67552215, 0, -1009116, 0, 6003, 0, 220, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [2, 6]}
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id: 9649181
{'degree': 16, 'field': [221319438916, 0, -18144187720, 0, 1351534256, 0, -44794140, 0, 2939261, 0, -12960, 0, 2846, 0, 20, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [4, 4]}
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id: 9649186
{'degree': 16, 'field': [5092320284689, 0, 447516446630, 0, 26370604117, 0, 543472336, 0, 19423910, 0, 409354, 0, 8320, 0, 92, 0, 1], 'lmfdb_label': '221760.lq4', 'torsion': [12]}
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ec_localdata • Show schema
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id: 5499150
{'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '221760.lq4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 5499151
{'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 30, 'j_denominator_valuation': 24, 'kodaira_symbol': -28, 'lmfdb_label': '221760.lq4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 5499152
{'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.lq4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 5499153
{'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221760.lq4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 5499154
{'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.lq4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 3080166
{'adelic_gens': [[12319, 18464, 6152, 18351], [1, 16, 0, 1], [18465, 16, 18464, 17], [13213, 16, 15584, 18165], [18479, 18464, 4612, 4491], [15, 2, 18382, 18467], [3376, 5, 6675, 18466], [5, 4, 18476, 18477], [6938, 4631, 11467, 9126], [1, 0, 16, 1], [3712, 5, 18435, 18466]], 'adelic_image': '18480.192.1.?', 'conductor': 221760, 'lmfdb_label': '221760.lq4', 'prime': 0}
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id: 813102
{'conductor': 221760, 'elladic_image': '16.24.0.9', 'lmfdb_label': '221760.lq4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 221760.lq does not appear in ec_padic