{
  "id": 6455,
  "curve_key": "3160162437291560848:-5553627254388551826888483520",
  "ainvs": [
    "0",
    "1",
    "0",
    "-65836717443574184",
    "6427809300263399540670276"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 127.79146531313005,
  "faltings_height": 8.520261380423369,
  "conductor": "377110594804217222471952",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "53",
    "71",
    "107",
    "131",
    "431",
    "433",
    "569",
    "577"
  ],
  "discriminant": "414691360480829914299335638015115331309536228926464",
  "regulator": "328142.813330603655385502025806427046606943680361251407",
  "points": [
    [
      "-295705490",
      "197703180756"
    ],
    [
      "124287040",
      "406268182254"
    ],
    [
      "164062570",
      "206065129536"
    ],
    [
      "596226880",
      "13383751017234"
    ],
    [
      "836762526",
      "23177907710412"
    ],
    [
      "5693586334/49",
      "201955863328596/343"
    ],
    [
      "4365218001310/62001",
      "22592295399246179156/15438249"
    ],
    [
      "5000678490736/22201",
      "5754641280940064502/3307949"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), with\r\nA=q(121q-99p)(26p-23q)(75p-44q),\r\nB=p(21q-74p)(25p-36q)(p+77q),\r\nat T=p/q=781/51.\r\n\r\nFamily equations as posted by wgxli with curve #4252:\r\nhttps://elliptic-rank.icarm.cloud/curve/4252\r\n\r\nSection formulas from the Layr-Labs elliptic-rank-challenge-public repository, submission/research/x400a-family.gp, commit 7482bf9:\r\nhttps://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf9/submission/research/x400a-family.gp\r\n\r\nRank bounds [8,8]. The eight displayed points were checked exactly on the global minimal model, and the torsion subgroup was computed as Z/2xZ/2.\r\n\r\nThe minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. The conductor is 377110594804217222471952.\r\n",
  "created_at": "2026-11-03 18:01:59",
  "updated_at": "2026-11-03 18:01:59"
}