Elliptic curve data - 186576.ds2

Formats: - HTML - YAML - JSON - 2025-10-09T17:40:10.395081

• 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': '186576bh', 'Clabel': '186576bh1', 'Cnumber': 1, 'abc_quality': 0.9824074196511602, 'absD': 266722904769627451392, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1196, 'ainvs': [0, 1, 0, -263696, -787571628], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 186576, 'degree': 8257536, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5988270350179805654886491719', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 96, 'isogeny_degrees': [1, 2], 'jinv': [-102568953241, 13490879103], 'lmfdb_iso': '186576.ds', 'lmfdb_label': '186576.ds2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -97, 5560], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '46.6.0.a.1', '52.6.0.c.1', '1196.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 3887], [3, 4, 2704], [13, 98, 1104], [23, 24, 8112]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.62320517572726688804467332966', 'prec': 103}, 'szpiro_ratio': 4.489880137168902, '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, 0, 1, 0, 4, 0, 2, 0, 1, 0, -2, 0, 0, 0, 4, 0, 2, 0, 6, 0], 'aplist': [0, 1, 4, 2, -2, 0, 2, 6, 1, 2, 4, -4, 6, 0, 0, 6, 0, -2, -14, 12, -14, -8, 10, -16, -4], 'class_deg': 2, 'class_size': 2, 'conductor': 186576, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '186576.ds', 'trace_hash': 1389899569824004471}
• 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': '0.0055295210863068264901066743243', 'prec': 110}, 'conductor': 186576, 'gens': [], 'heights': [], 'lmfdb_label': '186576.ds2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.077409667525761058992837194387', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.4313280824730616633123706611727775859', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[1018, 0, 1]], 'xcoord_integral_points': [1018]}
• lmfdb_label 186576.ds2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8225698
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '186576.ds2', 'torsion': [2, 2]}
  • id: 8225699
    {'degree': 4, 'field': [-23, 0, -5, 0, 1], 'lmfdb_label': '186576.ds2', 'torsion': [4]}
  • id: 8225702
    {'degree': 8, 'field': [-507, 0, 377, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '186576.ds2', 'torsion': [6]}
  • id: 8225701
    {'degree': 8, 'field': [81, 0, 117, 0, 112, 0, 13, 0, 1], 'lmfdb_label': '186576.ds2', 'torsion': [2, 4]}
  • id: 8225700
    {'degree': 8, 'field': [4888, 2054, -1609, -856, 344, 98, -28, -4, 1], 'lmfdb_label': '186576.ds2', 'torsion': [2, 4]}
  • id: 8225703
    {'degree': 16, 'field': [-225216, 1404288, -862592, -156032, 1188624, -810624, -271744, 358704, -82084, -24336, 14696, -1984, -474, 240, -20, -6, 1], 'lmfdb_label': '186576.ds2', 'torsion': [8]}
  • id: 8225704
    {'degree': 16, 'field': [23825961, -27370386, 32884074, -12226530, 9241299, -4132468, 2052950, -669856, 287366, -90106, 28898, -6848, 1930, -392, 76, -8, 1], 'lmfdb_label': '186576.ds2', '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: 4615897
    {'conductor': 186576, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '186576.ds2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4615898
    {'conductor': 186576, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '186576.ds2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 4615899
    {'conductor': 186576, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '186576.ds2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4615900
    {'conductor': 186576, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '186576.ds2', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 2862542
    {'adelic_gens': [[1, 0, 4, 1], [470, 1, 363, 0], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [1193, 4, 1192, 5], [301, 898, 896, 299], [93, 4, 186, 9]], 'adelic_image': '1196.12.0.?', 'conductor': 186576, 'lmfdb_label': '186576.ds2', 'prime': 0}
  • id: 697112
    {'conductor': 186576, 'elladic_image': '2.3.0.1', 'lmfdb_label': '186576.ds2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 186576.ds does not appear in ec_padic