Elliptic curve data - 5850.d1

Formats: - HTML - YAML - JSON - 2025-10-06T10:15:14.733342

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '5850m', 'Clabel': '5850m3', 'Cnumber': 3, 'abc_quality': 1.065548212916854, 'absD': 1264873866750000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [1, -1, 0, -4666392, -3878727984], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 5850, 'degree': 163840, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3221027528686460142714458794', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [986551739719628473, 111045168], 'lmfdb_iso': '5850.d', 'lmfdb_label': '5850.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -20739, 1140957], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0.h.1', '20.12.0-4.c.1.1', '60.24.0-12.h.1.1', '104.12.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], '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, 225], [3, 8, 650], [5, 14, 234], [13, 14, 450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.96807765231754098127344359432', 'prec': 103}, 'szpiro_ratio': 6.649756025930572, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, -1, 0, 1, 0, 0, -4, -1, 0, 0, 4, 0, -1, 4, 0, 1, 2, 0, -8, 0], 'aplist': [-1, 0, 0, -4, 4, -1, 2, -8, 0, -6, -4, 2, 10, -4, 8, -10, -4, -2, 16, 8, -2, 8, 12, -14, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 5850, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '5850.d', 'trace_hash': 308595188098084157}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.0096171674095240369286206809381', 'prec': 110}, 'conductor': 5850, 'gens': [], 'heights': [], 'lmfdb_label': '5850.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10271981972470922750184776815', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.82175855779767382001478214518894880162', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-4989, 4989, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': 'a', '5': 'a', '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '5850.d1'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 304731
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [2, 2]}
  • id: 304733
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '5850.d1', 'torsion': [4]}
  • id: 304732
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [4]}
  • id: 304734
    {'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [2, 4]}
  • id: 304735
    {'degree': 8, 'field': [9, 0, 0, 0, -21, 0, 0, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [2, 4]}
  • id: 304737
    {'degree': 8, 'field': [289, 0, -11, 0, 30, 0, 7, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [8]}
  • id: 304738
    {'degree': 8, 'field': [2164, -131, -1178, 47, 269, -19, -17, -2, 1], 'lmfdb_label': '5850.d1', 'torsion': [6]}
  • id: 304736
    {'degree': 8, 'field': [11664, 0, -1296, 0, 57, 0, -12, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [8]}
  • id: 304739
    {'degree': 16, 'field': [81, 0, 0, 0, 189, 0, 0, 0, 432, 0, 0, 0, 21, 0, 0, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [4, 4]}
  • id: 304741
    {'degree': 16, 'field': [19321, 0, 23120, 0, 4910, 0, 1656, 0, 1463, 0, -360, 0, 134, 0, -16, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [2, 8]}
  • id: 304744
    {'degree': 16, 'field': [59524, 68308, -24699, -102102, 91806, -58518, 34585, -11048, 435, 1500, -201, -132, 113, -70, 30, -8, 1], 'lmfdb_label': '5850.d1', 'torsion': [12]}
  • id: 304743
    {'degree': 16, 'field': [61504, 0, 6901, 0, 7162, 0, 2947, 0, -725, 0, 463, 0, -17, 0, 10, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [12]}
  • id: 304740
    {'degree': 16, 'field': [238144, -1229760, 3003856, -3757536, 2990974, -1703484, 685378, -195480, 43849, -9504, 5278, -1512, 580, -36, 28, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [2, 8]}
  • id: 304742
    {'degree': 16, 'field': [19131876, 0, -2106219, 0, -857978, 0, -641217, 0, 18495, 0, -1033, 0, 447, 0, -6, 0, 1], 'lmfdb_label': '5850.d1', 'torsion': [2, 6]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 115568
    {'conductor': 5850, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '5850.d1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 115569
    {'conductor': 5850, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '5850.d1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 115570
    {'conductor': 5850, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '5850.d1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 115571
    {'conductor': 5850, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '5850.d1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1702286
    {'adelic_gens': [[1, 0, 8, 1], [1291, 1290, 130, 1531], [824, 1245, 515, 934], [1, 8, 0, 1], [1, 4, 4, 17], [623, 0, 0, 1559], [7, 6, 1554, 1555], [1553, 8, 1552, 9], [1081, 320, 580, 1281], [976, 515, 355, 696]], 'adelic_image': '1560.48.0.?', 'conductor': 5850, 'lmfdb_label': '5850.d1', 'prime': 0}
  • id: 28872
    {'conductor': 5850, 'elladic_image': '4.6.0.1', 'lmfdb_label': '5850.d1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5850.d does not appear in ec_padic