Formats: - HTML - YAML - JSON - 2026-09-16T09:18:49.635617
  • ec_curvedata • Show schema
    {'Ciso': '42a', 'Clabel': '42a3', 'Cnumber': 3, 'abc_quality': 1.0649865394830864, 'absD': 63011844, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 56, 'ainvs': [1, 1, 1, -104, 101], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 16, 'elladic_images': ['8.96.0.50'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105447', 'prec': 97}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [124475734657, 63011844], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -104, 101], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.1', '8.96.0-8.f.1.1', '56.192.1-56.bp.2.4'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105447', 'prec': 97}, 'szpiro_ratio': 6.835108300244897, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, -1, 1, -2, -1, -1, 1, 1, -2, -4, -1, 6, -1, 2, 1, 2, 1, -4, -2], 'aplist': [1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10, -6, -4, 0, 6, 4, 6, 4, 8, 10, 0, -4, -6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 42, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '42.a', 'trace_hash': 1611795495172191507}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.68509183306601454759224479552', 'prec': 97}, 'conductor': 42, 'gens': [], 'heights': [], 'lmfdb_label': '42.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.7377237287484097558885933151', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '0.86886186437420487794429665753039351028', 'prec': 127}, 'tamagawa_product': 8, 'torsion_generators': [[1, -1, 1], [9, -5, 1]], 'xcoord_integral_points': [1, 9]}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [1, 1], '3': [0, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '42.a3'}
  • ec_torsion_growth • Show schema
    • id: 1272
      {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 4]}
    • id: 1273
      {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 4]}
    • id: 1274
      {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 4]}
    • id: 1276
      {'degree': 4, 'field': [-2, 0, 0, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 8]}
    • id: 1275
      {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [4, 4]}
    • id: 1277
      {'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 8]}
    • id: 1281
      {'degree': 8, 'field': [-4, 16, -16, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 6]}
    • id: 1280
      {'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [4, 8]}
    • id: 1278
      {'degree': 8, 'field': [16, 0, 0, 0, 1, 0, 0, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [4, 8]}
    • id: 1279
      {'degree': 8, 'field': [64, 0, 0, 0, 2, 0, 0, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 8]}
    • id: 1285
      {'degree': 16, 'field': [-1528, 5872, -164, -11320, 5258, 1272, -2663, 3512, -2344, 266, 477, -76, -139, 42, 14, -8, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 12]}
    • id: 1287
      {'degree': 16, 'field': [16, 0, 128, 0, 256, 0, -39, 0, -102, 0, 33, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 12]}
    • id: 1283
      {'degree': 16, 'field': [64, 0, 0, 0, -1024, 0, 0, 0, 318, 0, 0, 0, -16, 0, 0, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 16]}
    • id: 1282
      {'degree': 16, 'field': [256, 0, -768, 0, 1152, 0, -1392, 0, 1057, 0, -348, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [8, 8]}
    • id: 1284
      {'degree': 16, 'field': [256, 0, 704, 0, 968, 0, 600, 0, 68, 0, -144, 0, 50, 0, -10, 0, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 16]}
    • id: 1286
      {'degree': 16, 'field': [984, 4368, -2020, -10744, 23126, -29288, 25033, -17480, 10956, -6246, 3381, -1532, 589, -182, 46, -8, 1], 'lmfdb_label': '42.a3', 'torsion': [2, 12]}
  • ec_localdata • Show schema
    • id: 178
      {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42.a3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
    • id: 179
      {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '42.a3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 180
      {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '42.a3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • ec_galrep • Show schema
    • id: 1665971
      {'adelic_gens': [[1, 46, 0, 15], [3, 18, 10, 51], [49, 8, 48, 9], [1, 0, 8, 1], [5, 4, 52, 53], [17, 4, 0, 1], [1, 8, 0, 1]], 'adelic_image': '56.192.1.?', 'conductor': 42, 'lmfdb_label': '42.a3', 'prime': 0}
    • id: 110
      {'conductor': 42, 'elladic_image': '8.96.0.50', 'lmfdb_label': '42.a3', 'modell_image': '2Cs', 'prime': 2}
  • lmfdb_iso 42.a does not appear in ec_padic