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ec_curvedata • Show schema
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{'Ciso': '171941m', 'Clabel': '171941m1', 'Cnumber': 1, 'abc_quality': 0.8485979460414266, 'absD': 4305481773508055987, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 13398, 'ainvs': [0, -1, 1, -375503, 133580754], 'analytic_rank': 1, 'bad_primes': [7, 11, 29], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 171941, 'degree': 1935360, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2749772778485287481284150119', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 3], 'jinv': [-28094464000, 20657483], 'lmfdb_iso': '171941.m', 'lmfdb_label': '171941.m1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -63, 271], 'min_quad_twist_disc': 77, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '231.8.0.?', '406.2.0.?', '1218.8.0.?', '1914.8.0.?', '13398.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3381405362242333456738639727', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.10307456692168682354476685120', 'prec': 103}, 'szpiro_ratio': 4.225806595336829, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, -2, 0, 0, 0, 0, -2, 0, 0, 2, 2, 0, 0, 4, 6, 0, -7, 0], 'aplist': [0, -1, 0, 0, 0, 2, 6, -7, -3, -1, 4, 2, 9, 4, 9, 9, 6, 2, -13, -9, -1, 10, -6, 15, 7], 'class_deg': 3, 'class_size': 2, 'conductor': 171941, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '171941.m', 'trace_hash': 108101330093469024}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.010567684614001708068881312599', 'prec': 107}, 'conductor': 171941, 'gens': [[1104, 32609, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3381405362242333456738639727', 'prec': 100}], 'lmfdb_label': '171941.m1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22621633106734391136773237114', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2314045889958255182638659235052735520', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [1104]}
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lmfdb_label 171941.m1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 7635704
{'degree': 2, 'field': [-19, -1, 1], 'lmfdb_label': '171941.m1', 'torsion': [3]}
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id: 7635705
{'degree': 3, 'field': [-7, -7, -1, 1], 'lmfdb_label': '171941.m1', 'torsion': [2]}
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id: 7635708
{'degree': 6, 'field': [-227, 253, 138, -37, -6, -3, 1], 'lmfdb_label': '171941.m1', 'torsion': [6]}
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id: 7635706
{'degree': 6, 'field': [49, -189, 212, -47, 26, -3, 1], 'lmfdb_label': '171941.m1', 'torsion': [2, 2]}
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id: 7635707
{'degree': 6, 'field': [400, -116, 639, 62, -24, -2, 1], 'lmfdb_label': '171941.m1', 'torsion': [3]}
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id: 7635709
{'degree': 12, 'field': [-668554, 832384, -441996, -5332, 82064, -30604, 1636, 1160, 4, -162, 8, 0, 1], 'lmfdb_label': '171941.m1', 'torsion': [4]}
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id: 7635711
{'degree': 12, 'field': [3271, -7228, 10203, 4812, 17786, -19628, 6113, -2130, 1014, -10, -41, -2, 1], 'lmfdb_label': '171941.m1', 'torsion': [2, 6]}
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id: 7635710
{'degree': 12, 'field': [225625, 106875, 154175, -23400, 50749, 3661, 862, 49, -155, -48, 7, -1, 1], 'lmfdb_label': '171941.m1', 'torsion': [3, 3]}
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id: 7635713
{'degree': 18, 'field': [2675044, -116028, 1006810, 2257701, 10041131, 231600, 3271454, 2353393, 455827, -31913, 135735, 38169, -11169, 4015, 553, -228, 64, -9, 1], 'lmfdb_label': '171941.m1', 'torsion': [6]}
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id: 7635712
{'degree': 18, 'field': [866299303, -596527166049, 985750799454, 611388984823, 22844219658, -30968886162, -7810310227, -1898172795, 391857147, 92557993, -218724, 1118133, -798088, -38793, 19233, 398, -201, -3, 1], 'lmfdb_label': '171941.m1', 'torsion': [9]}
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ec_localdata • Show schema
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id: 4253402
{'conductor': 171941, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '171941.m1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 4253403
{'conductor': 171941, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '171941.m1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 4253404
{'conductor': 171941, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '171941.m1', 'prime': 29, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2772558
{'adelic_gens': [[7655, 10956, 8349, 6071], [3, 4, 8, 11], [4, 3, 9, 7], [13393, 6, 13392, 7], [1, 0, 6, 1], [4871, 0, 0, 13397], [6469, 2442, 7227, 7327], [11166, 4675, 2233, 4467], [1, 6, 0, 1]], 'adelic_image': '13398.16.0.?', 'conductor': 171941, 'lmfdb_label': '171941.m1', 'prime': 0}
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id: 648373
{'conductor': 171941, 'elladic_image': '3.4.0.1', 'lmfdb_label': '171941.m1', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 171941.m does not appear in ec_padic