Formats: - HTML - YAML - JSON - 2026-09-26T23:49:05.965794
  • ec_curvedata • Show schema
    {'Ciso': '1296e', 'Clabel': '1296e2', 'Cnumber': 2, 'abc_quality': 1.4265653296335434, 'absD': 4353564672, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 504, 'ainvs': [0, 0, 0, 405, -486], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 1296, 'degree': 432, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.53886632924398368439301861892', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [3375, 2], 'lmfdb_iso': '1296.g', 'lmfdb_label': '1296.g4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 3, -1], 'min_quad_twist_disc': 12, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '12.8.0-3.a.1.2', '21.64.1.a.2', '24.16.0-24.a.1.7', '28.16.0-7.a.1.1', '56.32.0-56.a.1.5', '63.192.5.e.2', '84.128.1.?', '168.256.5.?', '252.384.5.?', '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, 16]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2528931399840713164194587395', 'prec': 97}, 'szpiro_ratio': 4.1335436958520395, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 2, 0, 0, 0, -3, 0, 1, 0], 'aplist': [0, 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': 1296, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '1296.g', 'trace_hash': 111470209756918388}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.34036637824034343829847929677', 'prec': 97}, 'conductor': 1296, 'gens': [], 'heights': [], 'lmfdb_label': '1296.g4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.80848602428825605028754866728', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6169720485765121005750973345518439593', 'prec': 127}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [2, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [2, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1296.g4'}
  • ec_torsion_growth • Show schema
    • id: 64150
      {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [3]}
    • id: 64151
      {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [2]}
    • id: 64155
      {'degree': 6, 'field': [-12, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [6]}
    • id: 64154
      {'degree': 6, 'field': [1, 0, 9, 0, 6, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [7]}
    • id: 64153
      {'degree': 6, 'field': [2, 0, 0, -2, 0, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [3]}
    • id: 64152
      {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [2, 2]}
    • id: 64156
      {'degree': 12, 'field': [-8, 0, -33, 0, -27, 0, -6, 0, 6, 0, 3, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [4]}
    • id: 64159
      {'degree': 12, 'field': [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [21]}
    • id: 64157
      {'degree': 12, 'field': [1, 6, 21, 50, 78, 78, 47, 12, -6, -8, -3, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [3, 3]}
    • id: 64158
      {'degree': 12, 'field': [262, -108, 198, -268, 225, -180, 102, -36, 36, -16, 0, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [2, 6]}
    • id: 64160
      {'degree': 18, 'field': [-363, 0, 1134, 0, -1755, 0, 1494, 0, -1008, 0, 675, 0, -225, 0, 45, 0, -9, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [9]}
    • id: 64163
      {'degree': 18, 'field': [1, 0, 6, 0, -9, 0, -21, 0, 75, 0, -36, 0, -24, 0, 33, 0, -9, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [21]}
    • id: 64162
      {'degree': 18, 'field': [1, 0, 12, 0, 54, 0, 131, 0, 189, 0, 171, 0, 97, 0, 36, 0, 9, 0, 1], 'lmfdb_label': '1296.g4', 'torsion': [14]}
    • id: 64161
      {'degree': 18, 'field': [18, 0, 0, 18, 0, -54, 9, 18, -36, 6, 99, -18, 0, 54, -9, -18, 18, -6, 1], 'lmfdb_label': '1296.g4', 'torsion': [6]}
  • ec_localdata • Show schema
    • id: 19341
      {'conductor': 1296, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '1296.g4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
    • id: 19342
      {'conductor': 1296, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '1296.g4', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • ec_galrep • Show schema
    • id: 1672698
      {'adelic_gens': [[281, 392, 112, 393], [1, 426, 42, 253], [1, 216, 0, 1], [1, 0, 462, 1], [209, 462, 273, 293], [85, 42, 189, 43], [337, 168, 336, 169], [1, 0, 168, 1], [471, 350, 56, 375], [22, 321, 189, 169], [1, 42, 0, 73], [1, 0, 420, 1], [1, 168, 0, 1], [463, 282, 420, 295]], 'adelic_image': '504.768.21.?', 'conductor': 1296, 'lmfdb_label': '1296.g4', 'prime': 0}
    • id: 6224
      {'conductor': 1296, 'elladic_image': '8.2.0.1', 'lmfdb_label': '1296.g4', 'modell_image': '2G', 'prime': 2}
    • id: 6225
      {'conductor': 1296, 'elladic_image': '3.4.0.1', 'lmfdb_label': '1296.g4', 'modell_image': '3B', 'prime': 3}
    • id: 6226
      {'conductor': 1296, 'elladic_image': '7.8.0.1', 'lmfdb_label': '1296.g4', 'modell_image': '7B', 'prime': 7}
  • lmfdb_iso 1296.g does not appear in ec_padic