Formats: - HTML - YAML - JSON - 2026-10-05T15:53:05.918577
  • ec_curvedata • Show schema
    {'Ciso': '285c', 'Clabel': '285c1', 'Cnumber': 1, 'abc_quality': 0.9487490541305785, 'absD': 15582375, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 760, 'ainvs': [1, 1, 0, 23, -176], 'analytic_rank': 0, 'bad_primes': [3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 285, 'degree': 72, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.060991674266908690015084039524', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [1256216039, 15582375], 'lmfdb_iso': '285.c', 'lmfdb_label': '285.c4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 23, -176], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '20.12.0-4.c.1.2', '40.24.0-40.z.1.10', '76.12.0.?', '152.24.0.?', '190.6.0.?', '380.24.0.?', '760.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 95], [3, 4, 19], [5, 6, 57], [19, 20, 15]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.060991674266908690015084039524', 'prec': 97}, 'szpiro_ratio': 4.240360848514527, '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': '0.88516310764346563116930683019', 'prec': 97}, 'conductor': 285, 'gens': [], 'heights': [], 'lmfdb_label': '285.c4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0845657568691496664929197730', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6268486353037244997393796595007334708', 'prec': 127}, 'tamagawa_product': 6, 'torsion_generators': [[4, -2, 1]], 'xcoord_integral_points': [4]}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [1, 0], '3': [2, 0], '5': [1, 0], '19': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '285.c4'}
  • ec_torsion_growth • Show schema
    • id: 11862
      {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '285.c4', 'torsion': [4]}
    • id: 11863
      {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '285.c4', 'torsion': [4]}
    • id: 11861
      {'degree': 2, 'field': [24, -1, 1], 'lmfdb_label': '285.c4', 'torsion': [2, 2]}
    • id: 11865
      {'degree': 4, 'field': [-4, -6, 1, -1, 1], 'lmfdb_label': '285.c4', 'torsion': [8]}
    • id: 11864
      {'degree': 4, 'field': [36, 0, 7, 0, 1], 'lmfdb_label': '285.c4', 'torsion': [2, 4]}
    • id: 11869
      {'degree': 8, 'field': [-13, 25, -34, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '285.c4', 'torsion': [6]}
    • id: 11868
      {'degree': 8, 'field': [80, 20, -15, 35, 6, -1, 6, -1, 1], 'lmfdb_label': '285.c4', 'torsion': [2, 8]}
    • id: 11867
      {'degree': 8, 'field': [657, 606, 5, 76, 100, 0, 17, -2, 1], 'lmfdb_label': '285.c4', 'torsion': [8]}
    • id: 11866
      {'degree': 8, 'field': [3246, 1574, 1133, 680, 176, 40, 22, -2, 1], 'lmfdb_label': '285.c4', 'torsion': [2, 4]}
    • id: 11872
      {'degree': 16, 'field': [-882209, -193538, 1351580, 975000, -41120, -507844, -275298, -53240, 2475, 2260, 4572, 494, -125, 0, -25, -2, 1], 'lmfdb_label': '285.c4', 'torsion': [16]}
    • id: 11875
      {'degree': 16, 'field': [43, -191, -28, 616, 936, 1021, -237, -533, 1042, -969, 502, -260, 107, -42, 17, -4, 1], 'lmfdb_label': '285.c4', 'torsion': [12]}
    • id: 11871
      {'degree': 16, 'field': [676, -5876, 26126, -70914, 126721, -154042, 131088, -79022, 32172, -6734, -378, 1154, -344, 42, 14, -8, 1], 'lmfdb_label': '285.c4', 'torsion': [2, 8]}
    • id: 11874
      {'degree': 16, 'field': [2025, 0, -3240, 0, 1296, 0, -875, 0, 80, 0, -197, 0, 25, 0, -10, 0, 1], 'lmfdb_label': '285.c4', 'torsion': [12]}
    • id: 11870
      {'degree': 16, 'field': [6561, 0, 0, 0, 18306, 0, 0, 0, -749, 0, 0, 0, 226, 0, 0, 0, 1], 'lmfdb_label': '285.c4', 'torsion': [4, 4]}
    • id: 11873
      {'degree': 16, 'field': [44319145, 22111150, -16355001, -10882572, 3954066, 1546092, -133373, -296960, 37965, 21360, -1401, -1644, 365, -70, 30, -8, 1], 'lmfdb_label': '285.c4', 'torsion': [2, 6]}
  • ec_localdata • Show schema
    • id: 2571
      {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '285.c4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 2572
      {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '285.c4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
    • id: 2573
      {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '285.c4', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • ec_galrep • Show schema
    • id: 1666943
      {'adelic_gens': [[99, 98, 298, 675], [308, 1, 631, 6], [1, 0, 8, 1], [753, 8, 752, 9], [7, 6, 754, 755], [168, 3, 485, 2], [1, 8, 0, 1], [1, 4, 4, 17], [289, 288, 678, 295]], 'adelic_image': '760.48.0.?', 'conductor': 285, 'lmfdb_label': '285.c4', 'prime': 0}
    • id: 1162
      {'conductor': 285, 'elladic_image': '8.12.0.6', 'lmfdb_label': '285.c4', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 285.c does not appear in ec_padic