Elliptic curve data - 19.a2

Formats: - HTML - YAML - JSON - 2024-07-27T13:31:26.906401

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '19a', 'Clabel': '19a1', 'Cnumber': 1, 'abc_quality': 1.0331037033479094, 'absD': 6859, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 1026, 'ainvs': [0, 1, 1, -9, -15], 'analytic_rank': 0, 'bad_primes': [19], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 19, 'degree': 1, 'elladic_images': ['9.72.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.51586698734273704217752773488', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [-89915392, 6859], 'lmfdb_iso': '19.a', 'lmfdb_label': '19.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -9, -15], 'min_quad_twist_disc': 1, 'modell_images': ['3Cs.1.1'], 'modm_images': ['3.24.0-3.a.1.1', '9.72.0-9.b.1.1', '38.2.0.a.1', '114.48.1.?', '171.216.4.?', '342.432.13.?', '513.648.16.?', '1026.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.51586698734273704217752773488', 'prec': 107}, 'szpiro_ratio': 6.262043087240102, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, -2, -2, 3, 0, -1, 0, 1, 0, 3, 4, -4, 0, -6, 4, -3, 0, 1, -6], 'aplist': [0, -2, 3, -1, 3, -4, -3, 1, 0, 6, -4, 2, -6, -1, -3, 12, -6, -1, -4, 6, -7, 8, 12, 12, 8], 'class_deg': 9, 'class_size': 3, 'conductor': 19, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '19.a', 'trace_hash': 409437620317032020}
• 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': '2.8059270253215350687641816638', 'prec': 100}, 'conductor': 19, 'gens': [], 'heights': [], 'lmfdb_label': '19.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3597597334883108107365175612', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.45325324449610360357883918706482153450', 'prec': 133}, 'tamagawa_product': 3, 'torsion_generators': [[5, 9, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 3, 0], '3': [0, 1], '19': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '19.a2'}
• ec_torsion_growth •

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

  
  
  • id: 309
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '19.a2', 'torsion': [3, 3]}
  • id: 310
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '19.a2', 'torsion': [6]}
  • id: 311
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '19.a2', 'torsion': [2, 6]}
  • id: 312
    {'degree': 6, 'field': [4, -4, 4, -4, 2, 0, 1], 'lmfdb_label': '19.a2', 'torsion': [3, 6]}
  • id: 313
    {'degree': 9, 'field': [-1, 3, -4, 6, -1, -1, 2, -3, -1, 1], 'lmfdb_label': '19.a2', 'torsion': [9]}
  • id: 314
    {'degree': 12, 'field': [-2, -4, -4, -4, 6, 8, -4, 0, -4, -10, -2, 0, 1], 'lmfdb_label': '19.a2', 'torsion': [12]}
  • id: 315
    {'degree': 12, 'field': [1, -3, 5, -6, 3, 9, -14, 9, 3, -6, 5, -3, 1], 'lmfdb_label': '19.a2', 'torsion': [6, 6]}
  • id: 318
    {'degree': 18, 'field': [1, -3, 5, 0, -3, -17, 31, -5, -4, -12, 26, -18, 12, -9, 12, -1, 4, -1, 1], 'lmfdb_label': '19.a2', 'torsion': [3, 9]}
  • id: 316
    {'degree': 18, 'field': [1, 0, 0, 6, 0, 0, 7, 0, 0, -4, 0, 0, 10, 0, 0, -2, 0, 0, 1], 'lmfdb_label': '19.a2', 'torsion': [3, 9]}
  • id: 317
    {'degree': 18, 'field': [19683, 0, 0, -13851, 0, 0, 2700, 0, 0, -171, 0, 0, 100, 0, 0, -19, 0, 0, 1], 'lmfdb_label': '19.a2', 'torsion': [3, 9]}
• 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

  
  {'conductor': 19, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '19.a2', 'prime': 19, '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: 1665910
    {'adelic_gens': [[43, 30, 840, 85], [892, 27, 15, 676], [935, 790, 714, 553], [973, 54, 972, 55], [1, 27, 27, 730], [1, 54, 0, 1], [19, 54, 792, 469], [1, 0, 54, 1]], 'adelic_image': '1026.1296.43.?', 'conductor': 19, 'lmfdb_label': '19.a2', 'prime': 0}
  • id: 28
    {'conductor': 19, 'elladic_image': '9.72.0.3', 'lmfdb_label': '19.a2', 'modell_image': '3Cs.1.1', 'prime': 3}
• lmfdb_iso 19.a does not appear in ec_padic