Formats: - HTML - YAML - JSON - 2026-08-26T18:02:00.723126
  • ec_curvedata • Show schema
    {'Ciso': '9408k', 'Clabel': '9408k4', 'Cnumber': 4, 'abc_quality': 1.059886267720316, 'absD': 312264916992, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, 1503, 14337], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 9408, 'degree': 9216, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.89330829430446315887567767066', 'prec': 97}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 35, 'isogeny_degrees': [1, 2, 4], 'jinv': [97336, 81], 'lmfdb_iso': '9408.bj', 'lmfdb_label': '9408.bj4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 8, -8], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '24.24.0.n.1', '28.12.0-4.c.1.2', '56.24.0-8.d.1.2', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 49], [3, 4, 3136], [7, 26, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.94608075592312513044853885288', 'prec': 97}, 'szpiro_ratio': 3.6678800909369738, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 0, -1, 0, 2, 0, 0, 0, 1, 0, 4, 0, -2, 0, -2, 0, 6, 0, 4, 0], 'aplist': [0, -1, 2, 0, 4, -2, 6, 4, 0, -2, 4, 2, -2, 4, 8, -10, 4, 6, 4, 16, 6, -4, -12, -10, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 9408, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '9408.bj', 'trace_hash': 392084839546178773}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.16752602132161713018360674959', 'prec': 97}, 'conductor': 9408, 'gens': [], 'heights': [], 'lmfdb_label': '9408.bj4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.62615037298044477624558361039', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5046014919217791049823344415435781645', 'prec': 127}, 'tamagawa_product': 16, 'torsion_generators': [[-9, 0, 1]], 'xcoord_integral_points': [-9]}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': 'a', '3': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '9408.bj4'}
  • ec_torsion_growth • Show schema
    • id: 489102
      {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '9408.bj4', 'torsion': [4]}
    • id: 489103
      {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '9408.bj4', 'torsion': [4]}
    • id: 489101
      {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '9408.bj4', 'torsion': [2, 2]}
    • id: 489104
      {'degree': 4, 'field': [2, -8, 9, -2, 1], 'lmfdb_label': '9408.bj4', 'torsion': [2, 4]}
    • id: 489108
      {'degree': 8, 'field': [-7203, 0, 5488, 0, -294, 0, 0, 0, 1], 'lmfdb_label': '9408.bj4', 'torsion': [6]}
    • id: 489106
      {'degree': 8, 'field': [-26, 256, 52, -176, 42, 32, -8, -4, 1], 'lmfdb_label': '9408.bj4', 'torsion': [8]}
    • id: 489107
      {'degree': 8, 'field': [58, -104, 160, -128, 105, -52, 22, -4, 1], 'lmfdb_label': '9408.bj4', 'torsion': [8]}
    • id: 489105
      {'degree': 8, 'field': [81, 0, 76, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '9408.bj4', 'torsion': [2, 4]}
    • id: 489113
      {'degree': 16, 'field': [-22174, 165296, 63100, -205264, 4728, 127904, -35764, -48008, 19356, 11044, -4868, -1480, 618, 116, -40, -4, 1], 'lmfdb_label': '9408.bj4', 'torsion': [12]}
    • id: 489109
      {'degree': 16, 'field': [256, 0, -768, 0, 1152, 0, -1392, 0, 1057, 0, -348, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '9408.bj4', 'torsion': [4, 4]}
    • id: 489110
      {'degree': 16, 'field': [268, -1600, 4936, -1744, -10066, 8192, 8916, -17584, 15671, -10472, 5412, -2288, 806, -224, 52, -8, 1], 'lmfdb_label': '9408.bj4', 'torsion': [2, 8]}
    • id: 489112
      {'degree': 16, 'field': [834, 6408, 43612, 105712, 171808, 87616, -17084, -26312, -4876, 3812, 1232, -592, -70, 8, 28, -8, 1], 'lmfdb_label': '9408.bj4', 'torsion': [2, 6]}
    • id: 489111
      {'degree': 16, 'field': [2038, 984, 3076, 4776, 5138, 288, -48, -612, 527, -156, 396, -36, 110, -12, 16, 0, 1], 'lmfdb_label': '9408.bj4', 'torsion': [2, 8]}
    • id: 489114
      {'degree': 16, 'field': [2304, 0, -9216, 0, 16672, 0, -4608, 0, 669, 0, -144, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '9408.bj4', 'torsion': [12]}
  • ec_localdata • Show schema
    • id: 197740
      {'conductor': 9408, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '9408.bj4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
    • id: 197741
      {'conductor': 9408, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '9408.bj4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 197742
      {'conductor': 9408, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '9408.bj4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • ec_galrep • Show schema
    • id: 1726138
      {'adelic_gens': [[48, 7, 119, 132], [1, 0, 8, 1], [1, 8, 0, 1], [48, 7, 77, 90], [7, 6, 162, 163], [161, 8, 160, 9], [95, 0, 0, 167], [1, 4, 4, 17], [113, 56, 140, 57]], 'adelic_image': '168.48.0.?', 'conductor': 9408, 'lmfdb_label': '9408.bj4', 'prime': 0}
    • id: 45606
      {'conductor': 9408, 'elladic_image': '8.12.0.16', 'lmfdb_label': '9408.bj4', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 9408.bj does not appear in ec_padic