{
  "id": 3665,
  "curve_key": "10082439063392560801:-198684938843841003760055560049",
  "ainvs": [
    "1",
    "1",
    "1",
    "-210050813820678350",
    "229959419870628137482189067"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 134.9230357181066,
  "faltings_height": 9.300991680016741,
  "conductor": "1906431864891437910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "53",
    "89",
    "157",
    "173",
    "317",
    "3253"
  ],
  "discriminant": "-22251602290576149169521136749613131550573787537909760000",
  "regulator": "1175224.654861029311954531662723823714841104790808551",
  "points": [
    [
      "-706779663",
      "5035839823831"
    ],
    [
      "-663593673",
      "8782699502221"
    ],
    [
      "122324777",
      "14355961598551"
    ],
    [
      "-4401233669378111/26656569",
      "2219789865056601934420853/137627865747"
    ],
    [
      "-38177632703/81",
      "10917085684656799/729"
    ],
    [
      "-6476179607/9",
      "78813723800477/27"
    ],
    [
      "152929236103/324",
      "89586046963127087/5832"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -13/80 of the Elkies-Klagsbrun Z/4 fibration E2: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = -8(80t+9), c = 2(t-2)(2t-1)(18t-1)(2t-81) (arXiv:2003.00077, eq. (6)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:29:28",
  "updated_at": "2026-09-29 19:29:28"
}