Formats: - HTML - YAML - JSON - 2026-08-17T02:52:28.597780
  • ec_curvedata • Show schema
    {'Ciso': '1305c', 'Clabel': '1305c4', 'Cnumber': 4, 'abc_quality': 0.9529824634176626, 'absD': 2900294150625, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 6960, 'ainvs': [1, -1, 0, -3510, 115425], 'analytic_rank': 0, 'bad_primes': [3, 5, 29], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1305, 'degree': 2560, 'elladic_images': ['8.24.0.75'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0934255766907937330569549530', 'prec': 97}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [-6561258219361, 3978455625], 'lmfdb_iso': '1305.e', 'lmfdb_label': '1305.e3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -390, -4275], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0-4.d.1.4', '12.24.0-4.d.1.1', '24.48.0-24.z.1.2', '1160.48.0.?', '2320.96.0.?', '3480.96.1.?', '6960.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 145], [5, 6, 261], [29, 30, 45]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.54411943235673888735933233454', 'prec': 97}, 'szpiro_ratio': 5.132540931664702, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, 0, -1, -1, 0, -4, -3, 0, -1, 0, 0, 6, -4, 0, -1, -2, 0, 8, 1], 'aplist': [1, 0, -1, -4, 0, 6, -2, 8, 4, -1, 4, 6, -2, -4, 0, -6, 12, 6, -8, -16, -6, 12, 16, -2, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 1305, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1305.e', 'trace_hash': 625988075615584827}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.11226971271601711003664113789', 'prec': 97}, 'conductor': 1305, 'gens': [], 'heights': [], 'lmfdb_label': '1305.e3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.74405718460293353098531431139', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4881143692058670619706286227710821369', 'prec': 127}, 'tamagawa_product': 8, 'torsion_generators': [[-285, 285, 2]], 'xcoord_integral_points': []}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [2, 1], '3': 'a', '5': [0, 0], '29': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '1305.e3'}
  • ec_torsion_growth • Show schema
    • id: 64948
      {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [4]}
    • id: 64949
      {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '1305.e3', 'torsion': [4]}
    • id: 64947
      {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [2, 2]}
    • id: 64950
      {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [2, 4]}
    • id: 64954
      {'degree': 8, 'field': [-243, 0, 219, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [6]}
    • id: 64951
      {'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [4, 4]}
    • id: 64953
      {'degree': 8, 'field': [1296, 0, 36, 0, 37, 0, -1, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [8]}
    • id: 64952
      {'degree': 8, 'field': [1296, 0, 144, 0, -503, 0, -4, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [8]}
    • id: 64959
      {'degree': 16, 'field': [81, -324, 972, -1278, 1224, 189, -269, 212, 36, -194, 89, -18, 17, -14, 9, -4, 1], 'lmfdb_label': '1305.e3', 'torsion': [12]}
    • id: 64958
      {'degree': 16, 'field': [729, 0, -2271, 0, 1720, 0, 573, 0, -675, 0, -97, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [12]}
    • id: 64955
      {'degree': 16, 'field': [2916, 6804, 29430, -58410, 38125, -33052, 34010, -33492, 17350, -1658, 1534, -776, 142, -12, 8, -4, 1], 'lmfdb_label': '1305.e3', 'torsion': [2, 8]}
    • id: 64957
      {'degree': 16, 'field': [5929, 0, 41042, 0, 77065, 0, 58136, 0, 10030, 0, -166, 0, -80, 0, 8, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [2, 6]}
    • id: 64956
      {'degree': 16, 'field': [1679616, 0, 0, 0, -94608, 0, 0, 0, 4033, 0, 0, 0, -73, 0, 0, 0, 1], 'lmfdb_label': '1305.e3', 'torsion': [2, 8]}
  • ec_localdata • Show schema
    • id: 19612
      {'conductor': 1305, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '1305.e3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
    • id: 19613
      {'conductor': 1305, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1305.e3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 19614
      {'conductor': 1305, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1305.e3', 'prime': 29, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • ec_galrep • Show schema
    • id: 1672780
      {'adelic_gens': [[4177, 16, 2788, 65], [2641, 16, 3604, 65], [5, 16, 64, 205], [1, 16, 0, 1], [6945, 16, 6944, 17], [11, 4366, 1070, 3771], [1, 12, 4, 49], [1, 0, 16, 1], [6945, 6794, 3926, 3853], [2176, 4801, 4785, 2176]], 'adelic_image': '6960.192.3.?', 'conductor': 1305, 'lmfdb_label': '1305.e3', 'prime': 0}
    • id: 6306
      {'conductor': 1305, 'elladic_image': '8.24.0.75', 'lmfdb_label': '1305.e3', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 1305.e does not appear in ec_padic