Elliptic curve data - 4.4.1600.1-31.2-a4

Formats: - HTML - YAML - JSON - 2024-11-14T03:30:18.649956

• ec_nfcurves •

  Column	Type
  Lvalue	numeric
  abs_disc	bigint
  ainvs	text
  analytic_rank	smallint
  bad_primes	jsonb
  base_change	jsonb
  class_deg	integer
  class_label	text
  class_size	smallint
  cm	integer
  cm_type	smallint
  conductor_ideal	text
  conductor_label	text
  conductor_norm	bigint
  conductor_norm_factors	integer[]
  degree	smallint
  disc	text
  equation	text
  field_label	text
  galois_images	jsonb
  gens	jsonb
  heights	numeric[]
  iso_label	text
  iso_nlabel	smallint
  isodeg	integer[]
  isogeny_matrix	jsonb
  jinv	text
  label	text
  local_data	jsonb
  minD	text
  n_bad_primes	integer
  ngens	smallint
  non_min_p	jsonb
  nonmax_primes	smallint[]
  nonmax_rad	integer
  normdisc	numeric
  number	smallint
  omega	numeric
  potential_good_reduction	boolean
  q_curve	boolean
  rank	smallint
  rank_bounds	jsonb
  reducible_primes	integer[]
  reg	numeric
  root_analytic_conductor	double precision
  semistable	boolean
  sha	integer
  short_class_label	text
  short_label	text
  signature	jsonb
  tamagawa_product	integer
  torsion_gens	jsonb
  torsion_order	smallint
  torsion_primes	integer[]
  torsion_structure	jsonb
  trace_hash	bigint

  
  {'Lvalue': {'__RealLiteral__': 0, 'data': '1.06644587713377', 'prec': 54}, 'abs_disc': 1600, 'ainvs': '1,-2,0,1/2;-1,-2,1/2,1/2;-1,-1,1/2,1/2;-14,8,-10,-7;-4,48,-62,-73/2', 'analytic_rank': 0, 'bad_primes': ['(1/2*w^2+w-3)'], 'base_change': [], 'class_deg': 12, 'class_label': '4.4.1600.1-31.2-a', 'class_size': 8, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(1/2*w^2+w-3)', 'conductor_label': '31.2', 'conductor_norm': 31, 'conductor_norm_factors': [31], 'degree': 4, 'disc': '(3446*w^3+328*w^2+669*w-25209)', 'equation': '{y}^2+\\left(\\frac{1}{2}a^{3}-2a+1\\right){x}{y}+\\left(\\frac{1}{2}a^{3}+\\frac{1}{2}a^{2}-a-1\\right){y}={x}^{3}+\\left(\\frac{1}{2}a^{3}+\\frac{1}{2}a^{2}-2a-1\\right){x}^{2}+\\left(-7a^{3}-10a^{2}+8a-14\\right){x}-\\frac{73}{2}a^{3}-62a^{2}+48a-4', 'field_label': '4.4.1600.1', 'galois_images': ['2B', '3B'], 'gens': [], 'heights': [], 'iso_label': 'a', 'iso_nlabel': 0, 'isodeg': [1, 2, 3, 4, 6, 12], 'isogeny_matrix': [[1, 2, 12, 12, 4, 6, 3, 4], [2, 1, 6, 6, 2, 3, 6, 2], [12, 6, 1, 4, 3, 2, 4, 12], [12, 6, 4, 1, 12, 2, 4, 3], [4, 2, 3, 12, 1, 6, 12, 4], [6, 3, 2, 2, 6, 1, 2, 6], [3, 6, 4, 4, 12, 2, 1, 12], [4, 2, 12, 3, 4, 6, 12, 1]], 'jinv': '80704205874773584791012/787662783788549761,-95382125225553480591493/787662783788549761,-29872156558690483602305/1575325567577099522,18294256594913191872513/787662783788549761', 'label': '4.4.1600.1-31.2-a4', 'local_data': [{'p': '(1/2*w^2+w-3)', 'cp': 2, 'kod': 16, 'red': -1, 'normp': 31, 'rootno': 1, 'ord_cond': 1, 'ord_disc': 12, 'ord_den_j': 12}], 'minD': '(-7561/2*w^3+24553/2*w^2+8230*w-49762)', 'n_bad_primes': 1, 'ngens': 0, 'non_min_p': [], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'normdisc': -787662783788549761, 'number': 4, 'omega': {'__RealLiteral__': 0, 'data': '21.328917542675473882006677158657403896', 'prec': 130}, 'potential_good_reduction': False, 'q_curve': False, 'rank': 0, 'rank_bounds': [0, 0], 'reducible_primes': [2, 3], 'reg': 1, 'root_analytic_conductor': 5.4905867358050555, 'semistable': True, 'sha': 4, 'short_class_label': '31.2-a', 'short_label': '31.2-a4', 'signature': [4, 0], 'tamagawa_product': 2, 'torsion_gens': ['[[9/4,7,-3/2,-7/4],[23/8,-9/4,1/2,13/16],[1,0,0,0]]'], 'torsion_order': 2, 'torsion_primes': [2], 'torsion_structure': [2], 'trace_hash': 2070320677332490293}