Formats: - HTML - YAML - JSON - 2026-10-13T10:31:40.785545
  • ec_curvedata • Show schema
    {'Ciso': '162b', 'Clabel': '162b4', 'Cnumber': 4, 'abc_quality': 1.1259568215438134, 'absD': 68024448, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 504, 'ainvs': [1, -1, 1, -9695, -364985], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 162, 'degree': 126, 'elladic_images': ['8.2.0.1', '3.8.0.2', '7.16.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.81867422321169502752846286918', 'prec': 97}, 'faltings_index': 3, 'faltings_ratio': 21, 'intrinsic_torsion': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-189613868625, 128], 'lmfdb_iso': '162.c', 'lmfdb_label': '162.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -1077, 13877], 'min_quad_twist_disc': -3, 'modell_images': ['3B.1.2', '7B.2.3'], 'modm_images': ['3.8.0-3.a.1.1', '7.16.0-7.a.1.1', '8.2.0.a.1', '21.128.1-21.a.4.3', '24.16.0-24.a.1.6', '56.32.0-56.a.1.2', '63.384.5-63.e.1.3', '168.256.5.?', '504.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 81], [3, 2, 2], [7, 2, 81]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27993806545641466386678236774', 'prec': 97}, 'szpiro_ratio': 7.695501297976669, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, -3, 0, 2, 2, 0, 1, -3, 0, -1, 0], 'aplist': [1, 0, 0, 2, -3, 2, -3, -1, -6, 6, -4, -4, 9, -1, -6, 12, 3, 8, 5, -12, 11, -4, 12, 6, 5], 'class_deg': 21, 'class_size': 4, 'conductor': 162, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '162.c', 'trace_hash': 18950087430636185}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.19449507328019625045627388387', 'prec': 97}, 'conductor': 162, 'gens': [], 'heights': [], 'lmfdb_label': '162.c1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24056701963576719978850304313', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6839691374503703985195213018816543695', 'prec': 127}, 'tamagawa_product': 7, 'torsion_generators': [], 'xcoord_integral_points': []}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [4, 0], '3': 'a', '5': [0, 0, 0], '7': [0, 1]}, 'iwp0': 11, 'lmfdb_label': '162.c1'}
  • ec_torsion_growth • Show schema
    • id: 6471
      {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '162.c1', 'torsion': [3]}
    • id: 6472
      {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [2]}
    • id: 6473
      {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [3]}
    • id: 6475
      {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '162.c1', 'torsion': [3, 3]}
    • id: 6474
      {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [2, 2]}
    • id: 6477
      {'degree': 6, 'field': [12, -18, 9, 0, -3, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [6]}
    • id: 6476
      {'degree': 6, 'field': [224, -210, 63, -14, 0, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [7]}
    • id: 6478
      {'degree': 9, 'field': [-8, -12, -18, -21, -24, -9, -6, -3, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [6]}
    • id: 6479
      {'degree': 12, 'field': [-8, 0, 33, 0, -27, 0, 6, 0, 6, 0, -3, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [4]}
    • id: 6480
      {'degree': 12, 'field': [1, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [2, 6]}
    • id: 6481
      {'degree': 12, 'field': [343, 0, 0, -490, 0, 0, 224, 0, 0, -14, 0, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [21]}
    • id: 6483
      {'degree': 18, 'field': [1, -9, 33, -60, 60, -84, 222, -318, 153, 5, 153, -318, 222, -84, 60, -60, 33, -9, 1], 'lmfdb_label': '162.c1', 'torsion': [3, 6]}
    • id: 6485
      {'degree': 18, 'field': [18, 0, 0, 0, 0, 0, 9, 0, 18, 0, 63, 0, -48, 0, 27, 0, 12, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [2, 6]}
    • id: 6482
      {'degree': 18, 'field': [64, 0, 0, -240, 0, 0, 348, 0, 0, -2, 0, 0, 87, 0, 0, -15, 0, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [9]}
    • id: 6484
      {'degree': 18, 'field': [4096, -9216, -14544, 24816, 41316, -37440, -12764, 2652, 297, 5092, 105, -36, -102, -180, 18, -24, 9, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [14]}
    • id: 6486
      {'degree': 18, 'field': [32768, -147456, 313344, -402432, 390528, -331968, 245592, -142956, 69702, -31523, 12231, -2580, 198, 234, -132, 60, 0, -3, 1], 'lmfdb_label': '162.c1', 'torsion': [21]}
    • id: 6487
      {'degree': 21, 'field': [1, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '162.c1', 'torsion': [7]}
  • ec_localdata • Show schema
    • id: 1245
      {'conductor': 162, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '162.c1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
    • id: 1246
      {'conductor': 162, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '162.c1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • ec_galrep • Show schema
    • id: 1666432
      {'adelic_gens': [[281, 392, 112, 393], [73, 402, 0, 1], [1, 426, 42, 253], [39, 62, 56, 303], [1, 216, 0, 1], [1, 0, 462, 1], [85, 42, 189, 43], [337, 168, 336, 169], [1, 0, 168, 1], [295, 42, 231, 211], [22, 321, 189, 169], [1, 0, 420, 1], [1, 168, 0, 1], [463, 282, 420, 295]], 'adelic_image': '504.768.21.?', 'conductor': 162, 'lmfdb_label': '162.c1', 'prime': 0}
    • id: 646
      {'conductor': 162, 'elladic_image': '8.2.0.1', 'lmfdb_label': '162.c1', 'modell_image': '2G', 'prime': 2}
    • id: 647
      {'conductor': 162, 'elladic_image': '3.8.0.2', 'lmfdb_label': '162.c1', 'modell_image': '3B.1.2', 'prime': 3}
    • id: 648
      {'conductor': 162, 'elladic_image': '7.16.0.2', 'lmfdb_label': '162.c1', 'modell_image': '7B.2.3', 'prime': 7}
  • lmfdb_iso 162.c does not appear in ec_padic