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ec_curvedata • Show schema
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{'Ciso': '16940f', 'Clabel': '16940f2', 'Cnumber': 2, 'abc_quality': 0.9250517067496843, 'absD': 22645729624364000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 660, 'ainvs': [0, 1, 0, -1105980, -385073900], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 16940, 'degree': 414720, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4378574870919118548455465898', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [329890530231376, 49933296875], 'lmfdb_iso': '16940.a', 'lmfdb_label': '16940.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -9140, 285988], 'min_quad_twist_disc': -11, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0-6.a.1.10', '20.6.0.c.1', '33.8.0-3.a.1.2', '44.6.0.a.1', '60.48.0-60.q.1.3', '66.24.0-6.a.1.2', '132.48.0.?', '220.12.0.?', '660.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.77681173031942970986975338651', 'prec': 103}, 'szpiro_ratio': 5.480123071890572, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -2, 0, 1, 0, -1, 0, 1, 0, 0, 0, 4, 0, -2, 0, 0, 0, 4, 0], 'aplist': [0, -2, 1, -1, 0, 4, 0, 4, 6, 6, -4, 2, 6, 4, 6, -6, 0, 10, 2, 12, -8, 16, 12, -18, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 16940, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '16940.a', 'trace_hash': 212841677770867179}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0076296372746220018679003120160', 'prec': 110}, 'conductor': 16940, 'gens': [], 'heights': [], 'lmfdb_label': '16940.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14871360225012837208631109725', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7845632270015404650357331670483790409', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-785, 0, 1]], 'xcoord_integral_points': [-785]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [4, 0], '5': [1, 0], '7': [0, 0], '11': 'a'}, 'iwp0': 5, 'lmfdb_label': '16940.a3'}
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ec_torsion_growth • Show schema
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id: 868666
{'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [2, 2]}
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id: 868667
{'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '16940.a3', 'torsion': [6]}
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id: 868669
{'degree': 4, 'field': [9, 0, -5, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [2, 6]}
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id: 868668
{'degree': 4, 'field': [11, 0, 7, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [4]}
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id: 868670
{'degree': 6, 'field': [-1338, -228, 226, 5, -15, -1, 1], 'lmfdb_label': '16940.a3', 'torsion': [6]}
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id: 868671
{'degree': 8, 'field': [-175, -444, 956, -412, 118, 28, -12, -4, 1], 'lmfdb_label': '16940.a3', 'torsion': [2, 4]}
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id: 868673
{'degree': 8, 'field': [16, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [12]}
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id: 868672
{'degree': 8, 'field': [229, -374, 350, -22, 55, -22, -8, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [2, 4]}
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id: 868675
{'degree': 12, 'field': [-1826, 2156, 5790, -2618, -1970, 714, 31, 0, 141, -28, -17, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [2, 6]}
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id: 868674
{'degree': 12, 'field': [1296, -6480, 11808, -5040, 1216, 24, -445, 201, 24, 21, -4, -3, 1], 'lmfdb_label': '16940.a3', 'torsion': [3, 6]}
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id: 868678
{'degree': 16, 'field': [400, 800, 800, 800, 2264, 2768, 1808, 272, -151, -86, 18, -46, -13, -6, 0, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [2, 12]}
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id: 868677
{'degree': 16, 'field': [8825, -29740, 41520, -4788, -39306, 36016, 9488, -14620, -1129, 3072, -192, -636, 470, -196, 48, -8, 1], 'lmfdb_label': '16940.a3', 'torsion': [2, 12]}
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id: 868676
{'degree': 16, 'field': [133656721, 0, 6404772, 0, 10774698, 0, 7042024, 0, 1111075, 0, 36104, 0, 2178, 0, 52, 0, 1], 'lmfdb_label': '16940.a3', 'torsion': [8]}
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id: 868679
{'degree': 18, 'field': [19392699481, 63907256976, 89792589546, 44623250106, 17199158580, 424186941, 1193169131, -850364784, 178324776, -82953380, 16205181, -3713154, 756371, -98514, 18930, -1479, 231, -9, 1], 'lmfdb_label': '16940.a3', 'torsion': [18]}
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ec_localdata • Show schema
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id: 377748
{'conductor': 16940, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '16940.a3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 377749
{'conductor': 16940, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '16940.a3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
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id: 377750
{'conductor': 16940, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '16940.a3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 377751
{'conductor': 16940, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '16940.a3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1776893
{'adelic_gens': [[449, 2, 498, 13], [530, 657, 87, 8], [606, 397, 605, 386], [397, 12, 402, 73], [649, 12, 648, 13], [1, 12, 0, 1], [1, 6, 6, 37], [1, 0, 12, 1], [11, 2, 610, 651]], 'adelic_image': '660.96.1.?', 'conductor': 16940, 'lmfdb_label': '16940.a3', 'prime': 0}
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id: 79577
{'conductor': 16940, 'elladic_image': '2.3.0.1', 'lmfdb_label': '16940.a3', 'modell_image': '2B', 'prime': 2}
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id: 79578
{'conductor': 16940, 'elladic_image': '3.4.0.1', 'lmfdb_label': '16940.a3', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 16940.a does not appear in ec_padic