Elliptic curve data - 225420.l1

Formats: - HTML - YAML - JSON - 2025-09-28T05:12:38.880531

• 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': '225420y', 'Clabel': '225420y1', 'Cnumber': 1, 'abc_quality': 0.9363515015116128, 'absD': 2727824551920, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 510, 'ainvs': [0, -1, 0, -66430, -6568523], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 225420, 'degree': 814080, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4295417020564168898363278314', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 11, 'isogeny_degrees': [1], 'jinv': [-412435709457152, 34701615], 'lmfdb_iso': '225420.l', 'lmfdb_label': '225420.l1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -66430, -6568523], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['510.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 255], [3, 4, 75140], [5, 6, 15028], [13, 14, 17340], [17, 82, 780]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49018930585571443330153346978', 'prec': 103}, 'szpiro_ratio': 3.6448559088707273, '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, -3, 0, 1, 0, 5, 0, 1, 0, -1, 0, 0, 0, -7, 0], 'aplist': [0, -1, 1, -3, 5, 1, 0, -7, -4, 3, 0, 3, 3, -4, -3, -9, 8, -8, -2, 12, -7, 10, 8, -12, 2], 'class_deg': 1, 'class_size': 1, 'conductor': 225420, 'isogeny_matrix': [[1]], 'lmfdb_iso': '225420.l', 'trace_hash': 2223929573935552883}
• 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': '0.057321276640059473126110963443', 'prec': 107}, 'conductor': 225420, 'gens': [], 'heights': [], 'lmfdb_label': '225420.l1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14868794486783030239192370079', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1895035589426424191353896063003218709', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 225420.l1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9796582
    {'degree': 3, 'field': [-3, 0, -1, 1], 'lmfdb_label': '225420.l1', 'torsion': [2]}
  • id: 9796583
    {'degree': 6, 'field': [81, -27, 48, 21, -2, -2, 1], 'lmfdb_label': '225420.l1', 'torsion': [2, 2]}
  • id: 9796584
    {'degree': 8, 'field': [-10112688, 0, 655452, 0, -11016, 0, 0, 0, 1], 'lmfdb_label': '225420.l1', 'torsion': [3]}
  • id: 9796585
    {'degree': 12, 'field': [3832875, 1477190, -221270, -288302, -119953, -4982, 7962, 88, 56, 124, -24, -6, 1], 'lmfdb_label': '225420.l1', '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: 5591384
    {'conductor': 225420, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '225420.l1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5591385
    {'conductor': 225420, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '225420.l1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5591386
    {'conductor': 225420, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '225420.l1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5591387
    {'conductor': 225420, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '225420.l1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5591388
    {'conductor': 225420, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '225420.l1', '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.l1', 'prime': 0}
• lmfdb_iso 225420.l does not appear in ec_padic