Formats: - HTML - YAML - JSON - 2026-10-05T09:24:43.376738
  • ec_curvedata • Show schema
    {'Ciso': '19166a', 'Clabel': '19166a4', 'Cnumber': 4, 'abc_quality': 1.0082122835525031, 'absD': 2414841170339528, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 18648, 'ainvs': [1, 0, 0, -48628, -3387192], 'analytic_rank': 1, 'bad_primes': [2, 7, 37], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 19166, 'degree': 103680, 'elladic_images': ['8.6.0.6', '3.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6692537924111418340672075719', 'prec': 97}, 'faltings_index': 3, 'faltings_ratio': 6, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4956477625, 941192], 'lmfdb_iso': '19166.a', 'lmfdb_label': '19166.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -36, -70], 'min_quad_twist_disc': 37, 'modell_images': ['2B', '3Cs'], 'modm_images': ['2.3.0.a.1', '3.12.0.a.1', '6.36.0.a.1', '8.6.0.b.1', '24.72.1.h.1', '28.6.0.c.1', '56.12.0.k.1', '63.36.0.a.1', '84.72.1.?', '111.24.0.?', '126.108.2.?', '168.144.5.?', '222.72.0.?', '252.216.7.?', '504.432.21.?', '888.144.1.?', '2331.72.0.?', '3108.144.1.?', '4662.216.2.?', '6216.288.5.?', '9324.432.7.?', '18648.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8780463903026581211820776069', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 1369], [3, 2, 1369], [7, 8, 2738], [37, 686, 14]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.13620516391097038811684026362', 'prec': 97}, 'szpiro_ratio': 4.4610024623522815, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, -2, 1, 0, -2, 1, 1, 1, 0, 0, -2, 4, 1, 0, 1, -6, 1, -2, 0], 'aplist': [1, -2, 0, 1, 0, 4, -6, -2, 0, 6, 4, 0, 6, -8, -12, 6, 6, -8, -4, 0, 2, -8, -6, 6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 19166, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '19166.a', 'trace_hash': 108263830858770119}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.035489883859216434952673715796', 'prec': 97}, 'conductor': 19166, 'gens': [[-166, 426, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8780463903026581211820776069', 'prec': 97}], 'lmfdb_label': '19166.a3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.32573061108301131601708589796', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5056347851997556642322042115900514463', 'prec': 127}, 'tamagawa_product': 36, 'torsion_generators': [[-321, 321, 2]], 'xcoord_integral_points': [-166, 262, 2782]}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [2, 0], '3': [7, 1], '5': [1, 3, 0], '7': [2, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': 'a', '41': [1, 0], '43': [3, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '19166.a3'}
  • ec_torsion_growth • Show schema
    • id: 980891
      {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '19166.a3', 'torsion': [6]}
    • id: 980890
      {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 2]}
    • id: 980892
      {'degree': 2, 'field': [28, -1, 1], 'lmfdb_label': '19166.a3', 'torsion': [6]}
    • id: 980895
      {'degree': 4, 'field': [47, 22, -21, -2, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 6]}
    • id: 980894
      {'degree': 4, 'field': [81, 9, 10, -1, 1], 'lmfdb_label': '19166.a3', 'torsion': [3, 6]}
    • id: 980896
      {'degree': 4, 'field': [898, -52, 53, -2, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 6]}
    • id: 980893
      {'degree': 4, 'field': [2738, 0, -37, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [4]}
    • id: 980900
      {'degree': 8, 'field': [5467, 2534, -2026, -978, 395, 110, -32, -4, 1], 'lmfdb_label': '19166.a3', 'torsion': [12]}
    • id: 980899
      {'degree': 8, 'field': [10927, 2884, -2420, -896, 369, 92, -26, -4, 1], 'lmfdb_label': '19166.a3', 'torsion': [6, 6]}
    • id: 980897
      {'degree': 8, 'field': [15376, 0, -3744, 0, -602, 0, -8, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 4]}
    • id: 980901
      {'degree': 8, 'field': [40000, 0, -3400, 0, 278, 0, -17, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [12]}
    • id: 980898
      {'degree': 8, 'field': [444889, 0, -32002, 0, 1882, 0, -34, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 4]}
    • id: 980904
      {'degree': 16, 'field': [2738687, 9651600, -1781228, -12880744, -171164, 6481256, 98304, -1621128, 32929, 215800, -11964, -15456, 1302, 560, -60, -8, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 12]}
    • id: 980903
      {'degree': 16, 'field': [52758748, 43820980, -27467506, -29261602, 6475259, 8544258, -893790, -1449170, 94884, 155462, -9264, -10674, 778, 434, -42, -8, 1], 'lmfdb_label': '19166.a3', 'torsion': [3, 12]}
    • id: 980906
      {'degree': 16, 'field': [82064689, 50177204, -34673266, -27895512, 6589752, 7683256, -761754, -1326360, 76261, 148080, -8430, -10360, 756, 420, -40, -8, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 12]}
    • id: 980907
      {'degree': 16, 'field': [1169092864, 0, -107223040, 0, 16932112, 0, 1920544, 0, 134808, 0, -19168, 0, 1297, 0, -50, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 12]}
    • id: 980905
      {'degree': 16, 'field': [3259039744, 0, -26443776, 0, -2345248, 0, 2780032, 0, 63204, 0, -560, 0, 84, 0, -8, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [2, 12]}
    • id: 980902
      {'degree': 16, 'field': [17312243776, 0, -3810895744, 0, 43343506, 0, 16897052, 0, 1955085, 0, 147198, 0, 5676, 0, 114, 0, 1], 'lmfdb_label': '19166.a3', 'torsion': [8]}
    • id: 980908
      {'degree': 18, 'field': [-324643039, -458291694, 104952351, 332466644, -1863249, -112759509, -3733929, 23093922, 594861, -3089576, -10392, 275424, -6552, -15990, 834, 556, -45, -9, 1], 'lmfdb_label': '19166.a3', 'torsion': [18]}
    • id: 980909
      {'degree': 18, 'field': [24905932972416, -7526082983616, 7557131891232, -1783553009244, 962884128924, -182751851928, 69055855024, -10719910740, 3141006642, -402781493, 96510141, -10216944, 2055444, -174726, 29598, -1844, 258, -9, 1], 'lmfdb_label': '19166.a3', 'torsion': [18]}
  • ec_localdata • Show schema
    • id: 433146
      {'conductor': 19166, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '19166.a3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
    • id: 433147
      {'conductor': 19166, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '19166.a3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
    • id: 433148
      {'conductor': 19166, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '19166.a3', 'prime': 37, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • ec_galrep • Show schema
    • id: 1792141
      {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [1333, 12876, 16650, 667], [1, 6, 6, 37], [445, 14652, 11766, 12877], [17650, 12099, 15873, 16984], [19, 24, 1440, 1819], [18613, 36, 18612, 37], [9325, 14652, 0, 1037], [4031, 0, 0, 18647]], 'adelic_image': '18648.864.21.?', 'conductor': 19166, 'lmfdb_label': '19166.a3', 'prime': 0}
    • id: 89631
      {'conductor': 19166, 'elladic_image': '8.6.0.6', 'lmfdb_label': '19166.a3', 'modell_image': '2B', 'prime': 2}
    • id: 89632
      {'conductor': 19166, 'elladic_image': '3.12.0.1', 'lmfdb_label': '19166.a3', 'modell_image': '3Cs', 'prime': 3}
  • ec_padic • Show schema
    • id: 886254
      {'lmfdb_iso': '19166.a', 'p': 13, 'prec': 20, 'unit': 819756019544595554790, 'val': 1}
    • id: 886256
      {'lmfdb_iso': '19166.a', 'p': 17, 'prec': 20, 'unit': 155614124291569529590554, 'val': 1}
    • id: 886257
      {'lmfdb_iso': '19166.a', 'p': 19, 'prec': 20, 'unit': 67604982381205454141289, 'val': 2}
    • id: 886253
      {'lmfdb_iso': '19166.a', 'p': 29, 'prec': 20, 'unit': 3879749850552094660288981326, 'val': 1}
    • id: 886264
      {'lmfdb_iso': '19166.a', 'p': 31, 'prec': 20, 'unit': 17622678275850973852887507587, 'val': 1}
    • id: 886251
      {'lmfdb_iso': '19166.a', 'p': 41, 'prec': 20, 'unit': 4054329499237003964497136091554, 'val': 1}
    • id: 886252
      {'lmfdb_iso': '19166.a', 'p': 43, 'prec': 20, 'unit': 9719125592416674301273054031, 'val': 2}
    • id: 886262
      {'lmfdb_iso': '19166.a', 'p': 47, 'prec': 20, 'unit': 11983950675385584129534032194157, 'val': 1}
    • id: 886258
      {'lmfdb_iso': '19166.a', 'p': 53, 'prec': 20, 'unit': 428647967030011709831419967553862, 'val': 1}
    • id: 886259
      {'lmfdb_iso': '19166.a', 'p': 59, 'prec': 20, 'unit': 2180855717997148167253428326110202, 'val': 1}
    • id: 886263
      {'lmfdb_iso': '19166.a', 'p': 61, 'prec': 20, 'unit': 6302725397175612964057333128841535, 'val': 1}
    • id: 886250
      {'lmfdb_iso': '19166.a', 'p': 67, 'prec': 20, 'unit': 35900161851990162566775427547788984, 'val': 1}
    • id: 886260
      {'lmfdb_iso': '19166.a', 'p': 73, 'prec': 20, 'unit': 235296277524263292373552071401924986, 'val': 1}
    • id: 886255
      {'lmfdb_iso': '19166.a', 'p': 79, 'prec': 20, 'unit': 688545865597753074701163751201410223, 'val': 1}
    • id: 886249
      {'lmfdb_iso': '19166.a', 'p': 83, 'prec': 20, 'unit': 379994610206622419088055515998970738, 'val': 1}
    • id: 886261
      {'lmfdb_iso': '19166.a', 'p': 89, 'prec': 20, 'unit': 8937261591818118695723451751882306653, 'val': 1}
    • id: 886248
      {'lmfdb_iso': '19166.a', 'p': 97, 'prec': 20, 'unit': 13812931372219179879083650479051144531, 'val': 1}