Formats: - HTML - YAML - JSON - 2026-10-25T19:37:11.360910
  • ec_curvedata • Show schema
    {'Ciso': '150765w', 'Clabel': '150765w3', 'Cnumber': 3, 'abc_quality': 1.0982581996716574, 'absD': 21703708226665125, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 17480, 'ainvs': [1, 1, 0, -3177978, 2179257003], 'analytic_rank': 1, 'bad_primes': [3, 5, 19, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 150765, 'degree': 3548160, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3218859627914288448356925769', 'prec': 97}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 4], 'jinv': [23977812996389881, 146611125], 'lmfdb_iso': '150765.s', 'lmfdb_label': '150765.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -6007, -181724], 'min_quad_twist_disc': -23, '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', '92.12.0.?', '152.12.0.?', '460.24.0.?', '760.24.0.?', '3496.24.0.?', '17480.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9805047557415077635781801713', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 2, 2645], [3, 4, 10051], [5, 6, 30153], [19, 20, 7935], [23, 266, 285]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75413885482685399943231616099', 'prec': 97}, 'szpiro_ratio': 4.740971759554525, '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, 0, -2, 0, 6, -6, -8, -12, 14, 4, -14, 4, 0, -14, -16, 0, 6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 150765, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '150765.s', 'trace_hash': 7874826980847064}
  • ec_mwbsd • Show schema
    {'area': {'__RealLiteral__': 0, 'data': '0.0096213381265594090344489872847', 'prec': 97}, 'conductor': 150765, 'gens': [[1026, -399, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9805047557415077635781801713', 'prec': 97}], 'lmfdb_label': '150765.s1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.34035606521087035137623692850', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6963072231823818932957590260789548865', 'prec': 127}, 'tamagawa_product': 16, 'torsion_generators': [[4123, -4123, 2]], 'xcoord_integral_points': [-1482, 1026]}
  • lmfdb_label 150765.s1 does not appear in ec_iwasawa
  • ec_torsion_growth • Show schema
    • id: 6778351
      {'degree': 2, 'field': [-115, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [4]}
    • id: 6778350
      {'degree': 2, 'field': [-23, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [4]}
    • id: 6778349
      {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '150765.s1', 'torsion': [2, 2]}
    • id: 6778352
      {'degree': 4, 'field': [461, 48, -47, -2, 1], 'lmfdb_label': '150765.s1', 'torsion': [2, 4]}
    • id: 6778356
      {'degree': 8, 'field': [-257933, 169774, -65822, 17532, -3327, 441, -17, -2, 1], 'lmfdb_label': '150765.s1', 'torsion': [6]}
    • id: 6778354
      {'degree': 8, 'field': [-65123, -98268, -31164, 10488, 4565, -228, -138, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [8]}
    • id: 6778353
      {'degree': 8, 'field': [1116, -3924, 4050, -276, 199, -76, 30, -4, 1], 'lmfdb_label': '150765.s1', 'torsion': [2, 4]}
    • id: 6778355
      {'degree': 8, 'field': [130644900, 0, 4138300, 0, 50645, 0, 320, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [8]}
    • id: 6778358
      {'degree': 16, 'field': [-2417084, -1494312, 34009980, 66870120, -8761910, -84198120, -30871362, 13426008, 6001593, -833340, -429630, 22800, 14044, -228, -204, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [2, 8]}
    • id: 6778361
      {'degree': 16, 'field': [797449, 0, -1451647, 0, 1238224, 0, -475419, 0, 90177, 0, -10821, 0, 907, 0, -46, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [12]}
    • id: 6778357
      {'degree': 16, 'field': [3924361, 0, -1276728, 0, 562810, 0, 106632, 0, 59739, 0, 10728, 0, 1030, 0, 48, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [4, 4]}
    • id: 6778360
      {'degree': 16, 'field': [39077833805, 47778627320, 31238072821, 15159556258, 5430581039, 1629166053, 396116632, 81429058, 13729382, 1828221, 165296, -268, -2529, -670, -40, -4, 1], 'lmfdb_label': '150765.s1', 'torsion': [2, 6]}
    • id: 6778359
      {'degree': 16, 'field': [98879431401, 0, -7589183436, 0, 1459430572, 0, -126252468, 0, 15829550, 0, -769332, 0, 17852, 0, -204, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [2, 8]}
    • id: 6778362
      {'degree': 16, 'field': [311503515625, 0, -113409921875, 0, 19347250000, 0, -1485684375, 0, 56360625, 0, -1352625, 0, 22675, 0, -230, 0, 1], 'lmfdb_label': '150765.s1', 'torsion': [12]}
  • ec_localdata • Show schema
    • id: 3729313
      {'conductor': 150765, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '150765.s1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
    • id: 3729314
      {'conductor': 150765, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '150765.s1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
    • id: 3729315
      {'conductor': 150765, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '150765.s1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
    • id: 3729316
      {'conductor': 150765, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '150765.s1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • ec_galrep • Show schema
    • id: 2641879
      {'adelic_gens': [[7, 6, 17474, 17475], [17473, 8, 17472, 9], [1, 0, 8, 1], [1, 8, 0, 1], [5176, 15203, 13685, 16722], [1, 4, 4, 17], [14439, 0, 0, 17479], [1243, 5796, 5842, 11501], [11041, 11408, 6164, 10673], [13019, 13018, 1058, 12835]], 'adelic_image': '17480.48.0.?', 'conductor': 150765, 'lmfdb_label': '150765.s1', 'prime': 0}
    • id: 578389
      {'conductor': 150765, 'elladic_image': '4.6.0.1', 'lmfdb_label': '150765.s1', 'modell_image': '2B', 'prime': 2}
  • lmfdb_iso 150765.s does not appear in ec_padic