Formats: - HTML - YAML - JSON - 2026-09-22T19:42:44.771714
  • ec_curvedata • Show schema
    {'Ciso': '285c', 'Clabel': '285c3', 'Cnumber': 3, 'abc_quality': 1.0982581996716574, 'absD': 146611125, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 760, 'ainvs': [1, 1, 0, -6007, -181724], 'analytic_rank': 0, 'bad_primes': [3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 285, 'degree': 288, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75413885482685399943231616098', 'prec': 97}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [23977812996389881, 146611125], 'lmfdb_iso': '285.c', 'lmfdb_label': '285.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -6007, -181724], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '10.6.0.a.1', '20.24.0-20.g.1.1', '152.24.0.?', '760.48.0.?'], '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': True, 'serre_invariants': [[2, 2, 5], [3, 4, 19], [5, 6, 57], [19, 20, 15]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75413885482685399943231616098', 'prec': 97}, 'szpiro_ratio': 6.67244184577228, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, -1, -1, 1, -1, 4, -3, 1, 1, 4, 1, 2, 4, -1, -1, 2, 1, -1, -1], 'aplist': [1, -1, 1, 4, 4, 2, 2, -1, -4, -2, 0, -6, -6, 8, -12, -14, 4, 14, -4, 0, -14, 16, 0, -6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 285, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '285.c', 'trace_hash': 403871582455362642}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.22129077691086640779232670755', 'prec': 97}, 'conductor': 285, 'gens': [], 'heights': [], 'lmfdb_label': '285.c1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.54228287843457483324645988650', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6268486353037244997393796595007334708', 'prec': 127}, 'tamagawa_product': 12, 'torsion_generators': [[-181, 181, 2]], 'xcoord_integral_points': []}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [1, 1], '3': [2, 0], '5': [1, 0], '19': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '285.c1'}
  • ec_torsion_growth • Show schema
    • id: 11885
      {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '285.c1', 'torsion': [2, 2]}
    • id: 11887
      {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [4]}
    • id: 11886
      {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [4]}
    • id: 11889
      {'degree': 4, 'field': [-45, 0, 0, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [2, 4]}
    • id: 11888
      {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [2, 4]}
    • id: 11893
      {'degree': 8, 'field': [-13, 25, -34, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '285.c1', 'torsion': [6]}
    • id: 11890
      {'degree': 8, 'field': [121, 22, 2, -50, 31, -10, 8, -4, 1], 'lmfdb_label': '285.c1', 'torsion': [4, 4]}
    • id: 11891
      {'degree': 8, 'field': [900, 0, 700, 0, 365, 0, -40, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [8]}
    • id: 11892
      {'degree': 8, 'field': [50625, 0, -2700, 0, 315, 0, -12, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [8]}
    • id: 11896
      {'degree': 16, 'field': [-27869, 82956, -60820, -12380, 22385, 6648, -2842, -4020, -4220, 1620, -212, -172, 75, -40, 10, -4, 1], 'lmfdb_label': '285.c1', 'torsion': [2, 8]}
    • id: 11899
      {'degree': 16, 'field': [169, 0, -259, 0, 436, 0, -219, 0, -39, 0, 51, 0, -17, 0, 2, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [12]}
    • id: 11897
      {'degree': 16, 'field': [2025, 0, -3240, 0, 1296, 0, -875, 0, 80, 0, -197, 0, 25, 0, -10, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [2, 6]}
    • id: 11895
      {'degree': 16, 'field': [390625, 0, 0, 0, -84375, 0, 0, 0, 6400, 0, 0, 0, -135, 0, 0, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [2, 8]}
    • id: 11898
      {'degree': 16, 'field': [398649, -826920, 1598219, -1860802, 1789946, -1218974, 744277, -342920, 157845, -57060, 21015, -6044, 1705, -350, 70, -8, 1], 'lmfdb_label': '285.c1', 'torsion': [12]}
    • id: 11894
      {'degree': 16, 'field': [4100625, 0, 0, 0, -492075, 0, 0, 0, 20736, 0, 0, 0, -243, 0, 0, 0, 1], 'lmfdb_label': '285.c1', 'torsion': [2, 8]}
  • ec_localdata • Show schema
    • id: 2577
      {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '285.c1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 2578
      {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '285.c1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
    • id: 2579
      {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '285.c1', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • ec_galrep • Show schema
    • id: 1666940
      {'adelic_gens': [[99, 98, 298, 675], [1, 0, 8, 1], [753, 8, 752, 9], [7, 6, 754, 755], [1, 8, 0, 1], [1, 4, 4, 17], [616, 3, 5, 2], [401, 8, 84, 33], [483, 476, 522, 101]], 'adelic_image': '760.48.0.?', 'conductor': 285, 'lmfdb_label': '285.c1', 'prime': 0}
    • id: 1159
      {'conductor': 285, 'elladic_image': '4.12.0.8', 'lmfdb_label': '285.c1', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 285.c does not appear in ec_padic