Elliptic curve data - 2.2.8.1-686.1-d12

Formats: - HTML - YAML - JSON - 2024-04-18T09:18:36.888040

• 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': '2.1056856366902993881518569538570464891', 'prec': 130}, 'abs_disc': 8, 'ainvs': '1,0;1,-1;1,0;-164599,103060;-32816619,23909933', 'analytic_rank': 0, 'bad_primes': ['(w)', '(-2*w+1)', '(2*w+1)'], 'base_change': [], 'class_deg': 36, 'class_label': '2.2.8.1-686.1-d', 'class_size': 12, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(7*w+28)', 'conductor_label': '686.1', 'conductor_norm': 686, 'conductor_norm_factors': [2, 7], 'degree': 2, 'disc': '(-143248*w+1026368)', 'equation': '{y}^2+{x}{y}+{y}={x}^{3}+\\left(-a+1\\right){x}^{2}+\\left(103060a-164599\\right){x}+23909933a-32816619', 'field_label': '2.2.8.1', 'galois_images': ['2B', '3B'], 'gens': [], 'heights': [], 'iso_label': 'd', 'iso_nlabel': 3, 'isodeg': [1, 2, 3, 4, 6, 9, 12, 18, 36], 'isogeny_matrix': [[1, 9, 3, 36, 6, 12, 4, 18, 12, 2, 36, 4], [9, 1, 3, 4, 6, 12, 36, 2, 12, 18, 4, 36], [3, 3, 1, 12, 2, 4, 12, 6, 4, 6, 12, 12], [36, 4, 12, 1, 6, 12, 36, 2, 3, 18, 4, 9], [6, 6, 2, 6, 1, 2, 6, 3, 2, 3, 6, 6], [12, 12, 4, 12, 2, 1, 3, 6, 4, 6, 3, 12], [4, 36, 12, 36, 6, 3, 1, 18, 12, 2, 9, 4], [18, 2, 6, 2, 3, 6, 18, 1, 6, 9, 2, 18], [12, 12, 4, 3, 2, 4, 12, 6, 1, 6, 12, 3], [2, 18, 6, 18, 3, 6, 2, 9, 6, 1, 18, 2], [36, 4, 12, 4, 6, 3, 9, 2, 12, 18, 1, 36], [4, 36, 12, 9, 6, 12, 4, 18, 3, 2, 36, 1]], 'jinv': '9668307757341907702465000/2401,218768831290078842857759125/76832', 'label': '2.2.8.1-686.1-d12', 'local_data': [{'p': '(w)', 'cp': 9, 'kod': 13, 'red': 1, 'normp': 2, 'rootno': -1, 'ord_cond': 1, 'ord_disc': 9, 'ord_den_j': 9}, {'p': '(-2*w+1)', 'cp': 1, 'kod': 5, 'red': -1, 'normp': 7, 'rootno': 1, 'ord_cond': 1, 'ord_disc': 1, 'ord_den_j': 1}, {'p': '(2*w+1)', 'cp': 4, 'kod': -8, 'red': 0, 'normp': 7, 'rootno': -1, 'ord_cond': 2, 'ord_disc': 10, 'ord_den_j': 4}], 'minD': '(-143248*w+1026368)', 'n_bad_primes': 3, 'ngens': 0, 'non_min_p': [], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'normdisc': 1012391292416, 'number': 12, 'omega': {'__RealLiteral__': 0, 'data': '0.66175315233369934976592010281121399718', 'prec': 133}, 'potential_good_reduction': False, 'q_curve': True, 'rank': 0, 'rank_bounds': [0, 0], 'reducible_primes': [2, 3], 'reg': 1, 'root_analytic_conductor': 1.2934944687685523, 'semistable': False, 'sha': 1, 'short_class_label': '686.1-d', 'short_label': '686.1-d12', 'signature': [2, 0], 'tamagawa_product': 36, 'torsion_gens': ['[[1443/4,-199],[-1447/8,199/2],[1,0]]'], 'torsion_order': 2, 'torsion_primes': [2], 'torsion_structure': [2], 'trace_hash': 788073117808483933}