Elliptic curve data - 2.2.12.1-768.1-p3

Formats: - HTML - YAML - JSON - 2026-10-08T04:24:05.021065

• 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': '2.1985993056964826472999359845881297854', 'prec': 127}, 'abs_disc': 12, 'ainvs': '0,0;-1,-1;0,0;-3957,2286;134325,-77553', 'analytic_rank': 1, 'bad_primes': ['(w+1)', '(w)'], 'base_change': [], 'class_deg': 8, 'class_label': '2.2.12.1-768.1-p', 'class_size': 6, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(16*w)', 'conductor_label': '768.1', 'conductor_norm': 768, 'conductor_norm_factors': [2, 3], 'degree': 2, 'disc': '(-4608)', 'equation': '{y}^2={x}^{3}+\\left(-a-1\\right){x}^{2}+\\left(2286a-3957\\right){x}-77553a+134325', 'field_label': '2.2.12.1', 'galois_images': ['2Cs'], 'gens': ['[[6,-3],[-213,123],[1,0]]'], 'heights': [{'__RealLiteral__': 0, 'data': '0.42366800567945939665896357353120487811', 'prec': 127}], 'iso_label': 'p', 'iso_nlabel': 15, 'isodeg': [1, 2, 4], 'isogeny_matrix': [[1, 8, 4, 2, 8, 4], [8, 1, 2, 4, 4, 8], [4, 2, 1, 2, 2, 4], [2, 4, 2, 1, 4, 2], [8, 4, 2, 4, 1, 8], [4, 8, 4, 2, 8, 1]], 'jinv': '1989808/9,-1122088/9', 'label': '2.2.12.1-768.1-p3', 'local_data': [{'p': '(w+1)', 'cp': 4, 'kod': -10, 'red': 0, 'normp': 2, 'rootno': -1, 'ord_cond': 8, 'ord_disc': 18, 'ord_den_j': 0}, {'p': '(w)', 'cp': 2, 'kod': 8, 'red': -1, 'normp': 3, 'rootno': 1, 'ord_cond': 1, 'ord_disc': 4, 'ord_den_j': 4}], 'minD': '(4608)', 'n_bad_primes': 2, 'ngens': 1, 'non_min_p': [], 'nonmax_primes': [2], 'nonmax_rad': 2, 'normdisc': 21233664, 'number': 3, 'omega': {'__RealLiteral__': 0, 'data': '17.976744299323390120705109272463816060', 'prec': 127}, 'potential_good_reduction': False, 'q_curve': False, 'rank': 1, 'rank_bounds': [1, 1], 'reducible_primes': [2], 'reg': {'__RealLiteral__': 0, 'data': '0.42366800567945939665896357353120487811', 'prec': 127}, 'root_analytic_conductor': 1.6295567199298828, 'semistable': False, 'sha': 1, 'short_class_label': '768.1-p', 'short_label': '768.1-p3', 'signature': [2, 0], 'tamagawa_product': 8, 'torsion_gens': ['[[25,-14],[0,0],[1,0]]', '[[-51,30],[0,0],[1,0]]'], 'torsion_order': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2], 'trace_hash': 29535816221042865}