{
  "id": 6389,
  "curve_key": "28962556806993587008:-120836891916202886372514142720",
  "ainvs": [
    "0",
    "1",
    "0",
    "-603386600145699729",
    "139857513590772622141843311"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 134.4376065751426,
  "faltings_height": 9.217540243527631,
  "conductor": "3987245663666297209142592",
  "bad_primes": [
    "2",
    "3",
    "11",
    "107",
    "163",
    "313",
    "977",
    "1487",
    "2017",
    "10729"
  ],
  "discriminant": "5609431884807151068849191111737455056814520759587323904",
  "regulator": "12049829.407486093690474705952726317372294926913385320572",
  "points": [
    [
      "40780060386/25",
      "7390819898182809/125"
    ],
    [
      "1848985134642/1681",
      "1957799794316660085/68921"
    ],
    [
      "207131613",
      "4874807288340"
    ],
    [
      "240419741",
      "2947561990668"
    ],
    [
      "1832249749551/625",
      "2398625618733450576/15625"
    ],
    [
      "-824927043",
      "8731596017700"
    ],
    [
      "-389368137",
      "17769802541040"
    ],
    [
      "-493336569",
      "17817448079808"
    ],
    [
      "147321380895",
      "56544796308687984"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=-121/214. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [9,9]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:10:36",
  "updated_at": "2026-11-02 01:10:36"
}