Formats: - HTML - YAML - JSON - 2026-09-20T15:24:19.409325
  • ec_curvedata • Show schema
    {'Ciso': '240825cg', 'Clabel': '240825cg4', 'Cnumber': 4, 'abc_quality': 1.0982581996716574, 'absD': 11057248400783203125, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9880, 'ainvs': [1, 0, 1, -25381776, -49220665427], 'analytic_rank': 1, 'bad_primes': [3, 5, 13, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 240825, 'degree': 15925248, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8413324897746725547594395484', 'prec': 97}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 58, 'isogeny_degrees': [1, 2, 4], 'jinv': [23977812996389881, 146611125], 'lmfdb_iso': '240825.cg', 'lmfdb_label': '240825.cg1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -6007, -181724], 'min_quad_twist_disc': 65, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '10.6.0.a.1', '20.12.0.g.1', '52.12.0-4.c.1.1', '152.12.0.?', '260.24.0.?', '760.24.0.?', '1976.24.0.?', '9880.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '22.721487714028885725263906486', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 2, 4225], [3, 4, 80275], [5, 18, 9633], [13, 86, 1425], [19, 20, 12675]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75413885482685399943231616101', 'prec': 97}, 'szpiro_ratio': 5.064808845194554, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, 1, -1, 0, 1, 4, -3, 1, 0, -4, -1, 0, 4, 0, -1, -2, 1, 1, 0], 'aplist': [1, 1, 0, 4, -4, 0, -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': 240825, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '240825.cg', 'trace_hash': 2290685339875253125}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.0034044734909364062737281031931', 'prec': 97}, 'conductor': 240825, 'gens': [[135129893627, 44722832013779037, 3262]], 'heights': [{'__RealLiteral__': 0, 'data': '22.721487714028885725263906486', 'prec': 97}], 'lmfdb_label': '240825.cg1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.067261912898904483465662890962', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '12.226325820436314034090384645188179171', 'prec': 127}, 'tamagawa_product': 32, 'torsion_generators': [[-11657, 11653, 2]], 'xcoord_integral_points': []}
  • lmfdb_label 240825.cg1 does not appear in ec_iwasawa
  • ec_torsion_growth • Show schema
    • id: 10398806
      {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '240825.cg1', 'torsion': [2, 2]}
    • id: 10398807
      {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [4]}
    • id: 10398808
      {'degree': 2, 'field': [65, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [4]}
    • id: 10398809
      {'degree': 4, 'field': [209, -24, 25, -2, 1], 'lmfdb_label': '240825.cg1', 'torsion': [2, 4]}
    • id: 10398813
      {'degree': 8, 'field': [-7115575, -3369850, 400160, 114750, -5439, -1077, -17, -2, 1], 'lmfdb_label': '240825.cg1', 'torsion': [6]}
    • id: 10398810
      {'degree': 8, 'field': [711, 1908, -1944, 84, -71, 32, -6, -4, 1], 'lmfdb_label': '240825.cg1', 'torsion': [2, 4]}
    • id: 10398811
      {'degree': 8, 'field': [9801, 0, -8672, 0, 3334, 0, 112, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [8]}
    • id: 10398812
      {'degree': 8, 'field': [2165589, 348156, 106116, 20520, 3421, -228, -50, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [8]}
    • id: 10398817
      {'degree': 16, 'field': [-477036271, 136391219, 589303567, -69912569, -199331953, 18526170, 32550454, -2159864, -2281969, 268485, 65477, -19006, -18, 572, -40, -4, 1], 'lmfdb_label': '240825.cg1', 'torsion': [2, 6]}
    • id: 10398814
      {'degree': 16, 'field': [164836, 0, 195456, 0, 243940, 0, 47124, 0, -3171, 0, -1476, 0, 310, 0, -24, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [4, 4]}
    • id: 10398818
      {'degree': 16, 'field': [231617961, 0, 13714029, 0, 4834512, 0, 71017, 0, -77455, 0, 10063, 0, -173, 0, 26, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [12]}
    • id: 10398816
      {'degree': 16, 'field': [1993315789, -240769824, -170875722, 52678488, 93921196, -6252900, -10281162, 2443704, 1557501, -184908, -90078, 18696, 6304, -228, -132, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [2, 8]}
    • id: 10398819
      {'degree': 16, 'field': [4477617225, 0, 2476465245, 0, 540095796, 0, 65567525, 0, 4956665, 0, 240947, 0, 7375, 0, 130, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [12]}
    • id: 10398815
      {'degree': 16, 'field': [16284567321, 0, -860253804, 0, 245400412, 0, -12594132, 0, 425150, 0, 75372, 0, 4172, 0, 84, 0, 1], 'lmfdb_label': '240825.cg1', 'torsion': [2, 8]}
  • ec_localdata • Show schema
    • id: 5970117
      {'conductor': 240825, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '240825.cg1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
    • id: 5970118
      {'conductor': 240825, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '240825.cg1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
    • id: 5970119
      {'conductor': 240825, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '240825.cg1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
    • id: 5970120
      {'conductor': 240825, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '240825.cg1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • ec_galrep • Show schema
    • id: 3195291
      {'adelic_gens': [[9873, 8, 9872, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [859, 858, 8658, 7515], [2003, 2756, 3562, 3901], [1519, 0, 0, 9879], [5721, 2288, 9204, 9153], [3184, 5317, 2275, 8358], [7, 6, 9874, 9875]], 'adelic_image': '9880.48.0.?', 'conductor': 240825, 'lmfdb_label': '240825.cg1', 'prime': 0}
    • id: 873023
      {'conductor': 240825, 'elladic_image': '4.6.0.1', 'lmfdb_label': '240825.cg1', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 240825.cg does not appear in ec_padic