Formats: - HTML - YAML - JSON - 2026-10-12T19:34:16.460215
  • ec_curvedata • Show schema
    {'Ciso': '3234q', 'Clabel': '3234q2', 'Cnumber': 2, 'abc_quality': 1.1312493218569715, 'absD': 30195350250823296, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 616, 'ainvs': [1, 1, 1, -2570492, -1587302179], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 3234, 'degree': 75264, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2950804843514194788949783505', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [46546832455691959, 748268928], 'lmfdb_iso': '3234.r', 'lmfdb_label': '3234.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -52459, 4620209], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '88.6.0.?', '616.12.0.?'], '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': False, 'serre_invariants': [[2, 4, 77], [3, 4, 1078], [7, 20, 33], [11, 12, 294]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.83564787255993450006596379292', 'prec': 97}, 'szpiro_ratio': 6.916116972973272, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • ec_classdata • Show schema
    {'anlist': [0, 1, 1, -1, 1, 2, -1, 0, 1, 1, 2, 1, -1, 4, 0, -2, 1, 6, 1, 2, 2], 'aplist': [1, -1, 2, 0, 1, 4, 6, 2, 0, -6, 2, 2, -2, -12, -6, 10, 8, 4, 0, -8, 6, 12, 6, -12, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 3234, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '3234.r', 'trace_hash': 860559308438942810}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.010151224212455202874088148522', 'prec': 97}, 'conductor': 3234, 'gens': [], 'heights': [], 'lmfdb_label': '3234.r1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11923284550171183549030730076', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3385196740479313937286044213741964043', 'prec': 127}, 'tamagawa_product': 28, 'torsion_generators': [[-3693, 3689, 2]], 'xcoord_integral_points': []}
  • ec_iwasawa • Show schema
    {'iwdata': {'2': [4, 0], '3': [0, 0], '5': [0, 0], '7': 'a', '11': [1, 0]}, 'iwp0': 11, 'lmfdb_label': '3234.r1'}
  • ec_torsion_growth • Show schema
    • id: 168946
      {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '3234.r1', 'torsion': [2, 2]}
    • id: 168947
      {'degree': 4, 'field': [154, 0, -21, 0, 1], 'lmfdb_label': '3234.r1', 'torsion': [4]}
    • id: 168950
      {'degree': 8, 'field': [128, -704, 728, -49, 28, -7, 7, -4, 1], 'lmfdb_label': '3234.r1', 'torsion': [6]}
    • id: 168949
      {'degree': 8, 'field': [17424, 0, -286528, 0, -3410, 0, -88, 0, 1], 'lmfdb_label': '3234.r1', 'torsion': [2, 4]}
    • id: 168948
      {'degree': 8, 'field': [75625, 0, 550, 0, 26, 0, -26, 0, 1], 'lmfdb_label': '3234.r1', 'torsion': [2, 4]}
    • id: 168951
      {'degree': 16, 'field': [8161168, -24512080, 26183848, -16181800, 10846652, -5649328, 1656780, -158344, 84416, -22844, 3744, -638, 341, -44, -2, -2, 1], 'lmfdb_label': '3234.r1', 'torsion': [8]}
    • id: 168952
      {'degree': 16, 'field': [674576424, -476761824, 562738292, -160277440, 51621614, 32413648, -8010845, -1969496, -15714, 302814, -25233, -18548, 2515, 238, -14, -8, 1], 'lmfdb_label': '3234.r1', 'torsion': [2, 6]}
  • ec_localdata • Show schema
    • id: 58650
      {'conductor': 3234, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '3234.r1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
    • id: 58651
      {'conductor': 3234, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '3234.r1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 58652
      {'conductor': 3234, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '3234.r1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
    • id: 58653
      {'conductor': 3234, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3234.r1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • ec_galrep • Show schema
    • id: 1685055
      {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [613, 4, 612, 5], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 307, 0], [180, 1, 263, 0], [114, 1, 559, 0], [233, 386, 384, 231]], 'adelic_image': '616.12.0.?', 'conductor': 3234, 'lmfdb_label': '3234.r1', 'prime': 0}
    • id: 16245
      {'conductor': 3234, 'elladic_image': '2.3.0.1', 'lmfdb_label': '3234.r1', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 3234.r does not appear in ec_padic