Formats: - HTML - YAML - JSON - 2026-09-06T23:27:54.322788
  • ec_curvedata • Show schema
    {'Ciso': '690i', 'Clabel': '690i2', 'Cnumber': 2, 'abc_quality': 1.034205937070309, 'absD': 16171875000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2760, 'ainvs': [1, 0, 0, -786, -5940], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 690, 'degree': 480, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.66410244323211333308794349709', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2], 'jinv': [53706380371489, 16171875000], 'lmfdb_iso': '690.i', 'lmfdb_label': '690.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -786, -5940], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.c.1', '184.6.0.?', '2760.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 23], [3, 4, 115], [5, 6, 138], [23, 24, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.66410244323211333308794349709', 'prec': 97}, 'szpiro_ratio': 4.836476136819202, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, 1, 1, -1, 1, 0, 1, 1, -1, 2, 1, 0, 0, -1, 1, 6, 1, 4, -1], 'aplist': [1, 1, -1, 0, 2, 0, 6, 4, 1, 0, -8, -6, -2, -2, 4, -2, 0, -2, -2, -10, -10, 0, -4, 4, 16], 'class_deg': 2, 'class_size': 2, 'conductor': 690, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '690.i', 'trace_hash': 1486123207823667544}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.26495245439666118828869064337', 'prec': 97}, 'conductor': 690, 'gens': [], 'heights': [], 'lmfdb_label': '690.i1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.92267534889187543254844562975', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7680260466756262976453368892608701023', 'prec': 127}, 'tamagawa_product': 12, 'torsion_generators': [[-33, 33, 2]], 'xcoord_integral_points': []}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [2, 0], '3': [5, 0], '5': [0, 0], '23': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '690.i1'}
  • ec_torsion_growth • Show schema
    • id: 31949
      {'degree': 2, 'field': [-46, 0, 1], 'lmfdb_label': '690.i1', 'torsion': [2, 2]}
    • id: 31950
      {'degree': 4, 'field': [184, 0, -14, 0, 1], 'lmfdb_label': '690.i1', 'torsion': [4]}
    • id: 31953
      {'degree': 8, 'field': [-48, 0, 179, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '690.i1', 'torsion': [6]}
    • id: 31952
      {'degree': 8, 'field': [1932, 1104, -2668, 3128, -1563, -4, 6, -4, 1], 'lmfdb_label': '690.i1', 'torsion': [2, 4]}
    • id: 31951
      {'degree': 8, 'field': [42850, 15500, 5410, 4960, 1091, -56, -38, -4, 1], 'lmfdb_label': '690.i1', 'torsion': [2, 4]}
    • id: 31954
      {'degree': 16, 'field': [79506576, 44907696, -14042736, -16491744, 8124774, 1109334, -2754177, 759438, 390781, -113060, -28202, 2428, 2224, 70, -65, -2, 1], 'lmfdb_label': '690.i1', 'torsion': [8]}
    • id: 31955
      {'degree': 16, 'field': [4375822500, 0, 3061818900, 0, 693322425, 0, 28617300, 0, -1605288, 0, 62366, 0, -3084, 0, 0, 0, 1], 'lmfdb_label': '690.i1', 'torsion': [2, 6]}
  • ec_localdata • Show schema
    • id: 8522
      {'conductor': 690, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '690.i1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
    • id: 8523
      {'conductor': 690, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '690.i1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
    • id: 8524
      {'conductor': 690, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '690.i1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 8525
      {'conductor': 690, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '690.i1', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • ec_galrep • Show schema
    • id: 1669055
      {'adelic_gens': [[1, 2, 2, 5], [2402, 1, 1559, 0], [1, 4, 0, 1], [1841, 4, 922, 9], [2757, 4, 2756, 5], [1657, 4, 554, 9], [2, 1, 1379, 0], [1, 0, 4, 1], [1036, 1729, 345, 2416], [3, 4, 8, 11]], 'adelic_image': '2760.12.0.?', 'conductor': 690, 'lmfdb_label': '690.i1', 'prime': 0}
    • id: 3137
      {'conductor': 690, 'elladic_image': '2.3.0.1', 'lmfdb_label': '690.i1', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 690.i does not appear in ec_padic