Elliptic curve data - 259200.gl1

Formats: - HTML - YAML - JSON - 2026-07-07T09:07:38.680959

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '259200gl', 'Clabel': '259200gl1', 'Cnumber': 1, 'abc_quality': 0.6131471927654584, 'absD': 186624000000, 'adelic_genus': 0, 'adelic_index': 4, 'adelic_level': 60, 'ainvs': [0, 0, 0, -1800, 36000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 259200, 'degree': 322560, 'elladic_images': ['4.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.87755358287269641274090931393', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 167, 'isogeny_degrees': [1], 'jinv': [-3456, 1], 'lmfdb_iso': '259200.gl', 'lmfdb_label': '259200.gl1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -648, -7776], 'min_quad_twist_disc': -15, 'modell_images': [], 'modm_images': ['4.2.0.a.1', '60.4.0-4.a.1.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2025], [3, 6, 320], [5, 14, 10368]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2851432283316781479105304462', 'prec': 103}, 'szpiro_ratio': 2.768127606358226, '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, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 1, 0, 0, 0, 7, 0, 8, 0], 'aplist': [0, 0, 0, 4, 2, 1, 7, 8, -2, 9, -6, -7, -6, 6, -2, -6, 4, -1, 8, 12, 13, 10, 6, 5, 2], 'class_deg': 1, 'class_size': 1, 'conductor': 259200, 'isogeny_matrix': [[1]], 'lmfdb_iso': '259200.gl', 'trace_hash': 249408005637692880}
• 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': '0.17288871355105325986127941240', 'prec': 103}, 'conductor': 259200, 'gens': [], 'heights': [], 'lmfdb_label': '259200.gl1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.95761838054006441289574317346', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7457102832403864773744590407700355285', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 259200.gl1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11113611
    {'degree': 3, 'field': [-4, -3, 0, 1], 'lmfdb_label': '259200.gl1', 'torsion': [2]}
  • id: 11113612
    {'degree': 6, 'field': [2, 6, 9, -2, 0, 0, 1], 'lmfdb_label': '259200.gl1', 'torsion': [2, 2]}
  • id: 11113613
    {'degree': 8, 'field': [-4341, 452, 4, 348, 218, 4, 24, -4, 1], 'lmfdb_label': '259200.gl1', 'torsion': [3]}
  • id: 11113614
    {'degree': 12, 'field': [-57974, 216528, -422136, 279544, -58212, 19944, -8940, 396, -909, -92, 6, 0, 1], 'lmfdb_label': '259200.gl1', '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: 6424126
    {'conductor': 259200, 'conductor_valuation': 7, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '259200.gl1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6424127
    {'conductor': 259200, 'conductor_valuation': 4, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '259200.gl1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
  • id: 6424128
    {'conductor': 259200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '259200.gl1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 3306243
    {'adelic_gens': [[2, 3, 55, 53], [57, 4, 56, 5], [51, 55, 20, 41], [1, 4, 0, 1], [9, 20, 40, 49], [51, 40, 40, 11], [23, 0, 0, 59], [1, 0, 4, 1], [1, 2, 2, 5]], 'adelic_image': '60.4.0.?', 'conductor': 259200, 'lmfdb_label': '259200.gl1', 'prime': 0}
  • id: 930719
    {'conductor': 259200, 'elladic_image': '4.2.0.1', 'lmfdb_label': '259200.gl1', 'modell_image': '2G', 'prime': 2}
• lmfdb_iso 259200.gl does not appear in ec_padic