Elliptic curve data - 225420.v1

Formats: - HTML - YAML - JSON - 2025-09-29T11:39:56.145941

• 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': '225420j', 'Clabel': '225420j1', 'Cnumber': 1, 'abc_quality': 1.0934435884172249, 'absD': 1462965344180935920, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 510, 'ainvs': [0, 1, 0, -289606, 83479685], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 225420, 'degree': 3709440, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1892879653403584501295466930', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1], 'jinv': [-34172844524043008, 18610896399615], 'lmfdb_iso': '225420.v', 'lmfdb_label': '225420.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -289606, 83479685], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['510.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 8, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.86089633484730087985204219842', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 255], [3, 4, 75140], [5, 6, 3468], [13, 14, 17340], [17, 82, 780]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2499355691396559935947523314', 'prec': 100}, 'szpiro_ratio': 4.057019164574442, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 1, 0, -1, 0, -5, 0, 1, 0, -3, 0, 1, 0, -1, 0, 0, 0, -1, 0], 'aplist': [0, 1, -1, -5, -3, 1, 0, -1, -4, 1, -4, -7, 3, 6, -3, 5, 2, -6, -8, -8, -13, -4, 0, -8, 6], 'class_deg': 1, 'class_size': 1, 'conductor': 225420, 'isogeny_matrix': [[1]], 'lmfdb_iso': '225420.v', 'trace_hash': 1909639666187151523}
• 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': '0.012543208306577859036389511020', 'prec': 107}, 'conductor': 225420, 'gens': [[521, 8619, 1], [1421, 40443, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '0.26707167510197855917787533588', 'prec': 103}, {'__RealLiteral__': 0, 'data': '3.2603882493444323862983992304', 'prec': 100}], 'lmfdb_label': '225420.v1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.24998556612735356722666329600', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.912699458625975196636472002122359798', 'prec': 130}, 'tamagawa_product': 60, 'torsion_generators': [], 'xcoord_integral_points': [-415, 521, 5929, 6641]}
• lmfdb_label 225420.v1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9796462
    {'degree': 3, 'field': [-3, 0, -1, 1], 'lmfdb_label': '225420.v1', 'torsion': [2]}
  • id: 9796463
    {'degree': 6, 'field': [81, -27, 48, 21, -2, -2, 1], 'lmfdb_label': '225420.v1', 'torsion': [2, 2]}
  • id: 9796464
    {'degree': 8, 'field': [-403392, 75600, -77748, 4295, -2144, -7, 7, -4, 1], 'lmfdb_label': '225420.v1', 'torsion': [3]}
  • id: 9796465
    {'degree': 12, 'field': [-77886009, -27911574, 296262, 7981434, 3934848, 416970, -2244, 4524, 2587, -1194, 22, 0, 1], 'lmfdb_label': '225420.v1', 'torsion': [4]}
• 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: 5591284
    {'conductor': 225420, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '225420.v1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5591285
    {'conductor': 225420, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '225420.v1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 5591286
    {'conductor': 225420, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '225420.v1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5591287
    {'conductor': 225420, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '225420.v1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 5591288
    {'conductor': 225420, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '225420.v1', 'prime': 17, 'reduction_type': 0, '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

  
  {'adelic_gens': [[307, 2, 307, 3], [509, 2, 508, 3], [1, 1, 509, 0], [241, 2, 241, 3], [341, 2, 341, 3], [1, 0, 2, 1], [1, 2, 0, 1]], 'adelic_image': '510.2.0.?', 'conductor': 225420, 'lmfdb_label': '225420.v1', 'prime': 0}
• lmfdb_iso 225420.v does not appear in ec_padic