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ec_curvedata • Show schema
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{'Ciso': '121680dz', 'Clabel': '121680dz7', 'Cnumber': 7, 'abc_quality': 1.0818126452233845, 'absD': 1167434730049536000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -129796563, -569171178862], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 10616832, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0890939888411202034308407823', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [16778985534208729, 81000], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5334, -150368], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.96.1.dj.3', '40.12.0.v.1', '60.48.0.c.3', '104.12.0.?', '120.192.5.?', '156.48.0.?', '312.192.1.?', '520.24.0.?', '780.96.0.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.993925787616846496861917737', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232160', 'prec': 103}, 'szpiro_ratio': 5.778219606288636, '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, -6, 0, -4, 0], 'aplist': [0, 0, -1, -4, 0, 0, -6, -4, 0, 6, 8, -2, -6, 4, 0, 6, 0, -10, -4, 0, -2, -8, -12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 121680, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '121680.e', 'trace_hash': 1750704086879226857}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0020741829172213244609997329949', 'prec': 110}, 'conductor': 121680, 'gens': [[748903, 345940470, 7]], 'heights': [{'__RealLiteral__': 0, 'data': '10.993925787616846496861917737', 'prec': 100}], 'lmfdb_label': '121680.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.044728440533543035251926755706', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9339292465728431646689618320141460064', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-6578, 0, 1]], 'xcoord_integral_points': [-6578]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '121680.e1'}
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ec_torsion_growth • Show schema
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id: 5557682
{'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 2]}
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id: 5557685
{'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [6]}
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id: 5557683
{'degree': 2, 'field': [49, -1, 1], 'lmfdb_label': '121680.e1', 'torsion': [4]}
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id: 5557684
{'degree': 2, 'field': [78, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [4]}
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id: 5557688
{'degree': 4, 'field': [49, 0, -1, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [12]}
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id: 5557689
{'degree': 4, 'field': [361, 0, 14, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [12]}
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id: 5557686
{'degree': 4, 'field': [484, 0, 34, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 4]}
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id: 5557687
{'degree': 4, 'field': [529, 0, 6, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 6]}
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id: 5557690
{'degree': 6, 'field': [-6591, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [6]}
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id: 5557692
{'degree': 8, 'field': [276, -348, 25, 22, 44, 28, -10, -2, 1], 'lmfdb_label': '121680.e1', 'torsion': [8]}
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id: 5557694
{'degree': 8, 'field': [5041, 5820, 3972, 1320, 173, -60, -18, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 12]}
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id: 5557691
{'degree': 8, 'field': [30801, 86160, -32792, -2720, 2434, -80, -88, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 4]}
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id: 5557693
{'degree': 8, 'field': [80089, 0, 11436, 0, 890, 0, 36, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [24]}
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id: 5557698
{'degree': 12, 'field': [140625, 0, 0, 0, 0, 0, 8688, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [12]}
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id: 5557697
{'degree': 12, 'field': [1058841, 0, 0, 0, 0, 0, -438, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [12]}
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id: 5557695
{'degree': 12, 'field': [4813636, 0, 2242968, 0, 427245, 0, 43946, 0, 2535, 0, 78, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [3, 6]}
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id: 5557696
{'degree': 12, 'field': [31259281, 0, -20373000, 0, -1827300, 0, -33182, 0, 1500, 0, -60, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 6]}
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id: 5557703
{'degree': 16, 'field': [76176, 0, 107304, 0, 40225, 0, -15684, 0, -636, 0, 1526, 0, 300, 0, 24, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [24]}
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id: 5557700
{'degree': 16, 'field': [80271, -53892, 198378, -270468, 95358, 31188, 13894, -14324, -3537, 3308, 566, -420, -112, 56, 12, -8, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 8]}
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id: 5557701
{'degree': 16, 'field': [17598025, 0, 12357420, 0, 3878014, 0, 475824, 0, 7359, 0, -2712, 0, 706, 0, -36, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 24]}
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id: 5557699
{'degree': 16, 'field': [203661441, -181527120, 80899200, -57834000, 16040194, 1059160, 896000, -238560, -86649, 37640, 800, 2240, 134, -40, 0, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [4, 4]}
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id: 5557702
{'degree': 16, 'field': [1763244081, 0, 226764096, 0, 110224072, 0, 11270168, 0, 1605150, 0, 119392, 0, 4872, 0, 104, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [2, 12]}
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id: 5557704
{'degree': 18, 'field': [13178301152, 4150679520, 9761599536, 1845897760, 3063158280, 324817800, 520017332, 29282160, 53707704, 1286660, 3652644, 15360, 172033, -720, 5571, -20, 111, 0, 1], 'lmfdb_label': '121680.e1', 'torsion': [18]}
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ec_localdata • Show schema
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id: 2995199
{'conductor': 121680, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '121680.e1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 2995200
{'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '121680.e1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 2995201
{'conductor': 121680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '121680.e1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 2995202
{'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121680.e1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2457878
{'adelic_gens': [[352, 1443, 117, 274], [1169, 936, 1170, 1559], [1002, 559, 1157, 92], [1, 12, 12, 145], [1537, 24, 1536, 25], [479, 0, 0, 1559], [1299, 676, 832, 987], [15, 106, 254, 131], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '1560.384.5.?', 'conductor': 121680, 'lmfdb_label': '121680.e1', 'prime': 0}
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id: 477384
{'conductor': 121680, 'elladic_image': '4.6.0.1', 'lmfdb_label': '121680.e1', 'modell_image': '2B', 'prime': 2}
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id: 477385
{'conductor': 121680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '121680.e1', 'modell_image': '3B', 'prime': 3}
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ec_padic • Show schema
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id: 6361699
{'lmfdb_iso': '121680.e', 'p': 7, 'prec': 20, 'unit': 3655126417512847, 'val': 1}
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id: 6361704
{'lmfdb_iso': '121680.e', 'p': 17, 'prec': 20, 'unit': 157486403324793425271999, 'val': 1}
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id: 6361695
{'lmfdb_iso': '121680.e', 'p': 19, 'prec': 20, 'unit': 1465719948403277590253664, 'val': 1}
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id: 6361702
{'lmfdb_iso': '121680.e', 'p': 29, 'prec': 20, 'unit': 1210003974022209909380232618, 'val': 1}
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id: 6361710
{'lmfdb_iso': '121680.e', 'p': 31, 'prec': 20, 'unit': 519916441349091585730491626, 'val': 1}
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id: 6361698
{'lmfdb_iso': '121680.e', 'p': 37, 'prec': 20, 'unit': 320824555419521225653657006687, 'val': 1}
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id: 6361700
{'lmfdb_iso': '121680.e', 'p': 41, 'prec': 20, 'unit': 1006818582697798013754455184026, 'val': 1}
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id: 6361701
{'lmfdb_iso': '121680.e', 'p': 43, 'prec': 20, 'unit': 154738038948532199300645832436, 'val': 1}
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id: 6361706
{'lmfdb_iso': '121680.e', 'p': 53, 'prec': 20, 'unit': 434237483939887250325972754640005, 'val': 1}
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id: 6361709
{'lmfdb_iso': '121680.e', 'p': 61, 'prec': 20, 'unit': 6444350278983481418665141482497898, 'val': 1}
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id: 6361697
{'lmfdb_iso': '121680.e', 'p': 67, 'prec': 20, 'unit': 22832319830563244966439552818854775, 'val': 1}
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id: 6361707
{'lmfdb_iso': '121680.e', 'p': 73, 'prec': 20, 'unit': 20544479874469637442433102095691288, 'val': 1}
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id: 6361703
{'lmfdb_iso': '121680.e', 'p': 79, 'prec': 20, 'unit': 195501196714420863351160941671496151, 'val': 1}
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id: 6361705
{'lmfdb_iso': '121680.e', 'p': 83, 'prec': 20, 'unit': 796565802152685252515251970240006901, 'val': 1}
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id: 6361708
{'lmfdb_iso': '121680.e', 'p': 89, 'prec': 20, 'unit': 2976206864814925705708995924057961043, 'val': 1}
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id: 6361696
{'lmfdb_iso': '121680.e', 'p': 97, 'prec': 20, 'unit': 43208109913718632311793379341079283355, 'val': 1}