Formats: - HTML - YAML - JSON - 2026-07-20T22:02:48.136844
  • ec_curvedata • Show schema
    {'Ciso': '550b', 'Clabel': '550b2', 'Cnumber': 2, 'abc_quality': 1.0129363433875729, 'absD': 25164218750, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 440, 'ainvs': [1, 0, 1, -148501, -22038602], 'analytic_rank': 0, 'bad_primes': [2, 5, 11], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 550, 'degree': 2400, 'elladic_images': ['5.24.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4497945369798716774886669571', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'intrinsic_torsion': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 5], 'jinv': [-23178622194826561, 1610510], 'lmfdb_iso': '550.f', 'lmfdb_label': '550.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5940, -178685], 'min_quad_twist_disc': 5, 'modell_images': ['5B.1.3'], 'modm_images': ['5.24.0-5.a.2.1', '440.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 275], [5, 18, 2], [11, 12, 50]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.64507558076282149018828729049', 'prec': 103}, 'szpiro_ratio': 7.502257921418977, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
  • ec_classdata • Show schema
    {'anlist': [0, 1, -1, 1, 1, 0, -1, -3, -1, -2, 0, 1, 1, 6, 3, 0, 1, 7, 2, 5, 0], 'aplist': [-1, 1, 0, -3, 1, 6, 7, 5, 6, 5, -3, -3, 2, -4, 2, 1, -10, 7, -8, 7, -14, 10, 6, -15, 12], 'class_deg': 5, 'class_size': 2, 'conductor': 550, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '550.f', 'trace_hash': 302784965514392083}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.055045835176599840974915341407', 'prec': 107}, 'conductor': 550, 'gens': [], 'heights': [], 'lmfdb_label': '550.f1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12160111663786428999042866119', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2160111663786428999042866118621373262', 'prec': 130}, 'tamagawa_product': 10, 'torsion_generators': [], 'xcoord_integral_points': []}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [3, 0], '3': [6, 0], '5': 'a', '7': [0, 0], '11': [1, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '550.f1'}
  • ec_torsion_growth • Show schema
    • id: 24722
      {'degree': 3, 'field': [-8, 2, 0, 1], 'lmfdb_label': '550.f1', 'torsion': [2]}
    • id: 24723
      {'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '550.f1', 'torsion': [5]}
    • id: 24724
      {'degree': 6, 'field': [16, -32, 118, 16, -7, -2, 1], 'lmfdb_label': '550.f1', 'torsion': [2, 2]}
    • id: 24725
      {'degree': 8, 'field': [-75, 0, -280, 0, -30, 0, 0, 0, 1], 'lmfdb_label': '550.f1', 'torsion': [3]}
    • id: 24726
      {'degree': 10, 'field': [-320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '550.f1', 'torsion': [5]}
    • id: 24727
      {'degree': 12, 'field': [-22256, 12632, 28339, 29468, -3711, -4172, 273, 80, 181, -60, 7, -4, 1], 'lmfdb_label': '550.f1', 'torsion': [4]}
    • id: 24728
      {'degree': 12, 'field': [1, 3, -3, -11, 20, 67, 32, -13, 30, -11, 7, -2, 1], 'lmfdb_label': '550.f1', 'torsion': [10]}
    • id: 24729
      {'degree': 20, 'field': [32000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '550.f1', 'torsion': [5, 5]}
  • ec_localdata • Show schema
    • id: 6224
      {'conductor': 550, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '550.f1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
    • id: 6225
      {'conductor': 550, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '550.f1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
    • id: 6226
      {'conductor': 550, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '550.f1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • ec_galrep • Show schema
    • id: 1668285
      {'adelic_gens': [[103, 210, 265, 149], [431, 10, 430, 11], [1, 0, 10, 1], [1, 10, 0, 1], [111, 10, 0, 1], [221, 10, 225, 51], [321, 10, 285, 51], [6, 13, 385, 321]], 'adelic_image': '440.48.1.?', 'conductor': 550, 'lmfdb_label': '550.f1', 'prime': 0}
    • id: 2463
      {'conductor': 550, 'elladic_image': '5.24.0.4', 'lmfdb_label': '550.f1', 'modell_image': '5B.1.3', 'prime': 5}
  • lmfdb_iso 550.f does not appear in ec_padic