{
  "id": 6454,
  "curve_key": "292764349800557007704516416:-4110807340715660889168124285578285438464",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-6099257287511604327177425",
    "4757878866571085040818203272713556177"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 182.8242307511572,
  "faltings_height": 13.238550548094194,
  "conductor": "2031996162762000342302590303680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "47",
    "59",
    "67",
    "107",
    "137",
    "727",
    "1009",
    "3527"
  ],
  "discriminant": "4742116784884200346899309928315753577707877021661379793338624445124864000000",
  "regulator": "64169287.91882239654000836872981984840827655217920977013650",
  "points": [
    [
      "-1988904913816",
      "3003518844742934925"
    ],
    [
      "-420076285141",
      "2691821656907905500"
    ],
    [
      "822872938379",
      "544195479366777780"
    ],
    [
      "2009879008009",
      "786285132121174400"
    ],
    [
      "3016123945729",
      "3714761563247579680"
    ],
    [
      "5255657149433",
      "10856964514752317520"
    ],
    [
      "94888560354491/49",
      "156661631598868472700/343"
    ],
    [
      "379625316772423/49",
      "7050549873707555860112/343"
    ],
    [
      "767144431266689/121",
      "19783732754981791908000/1331"
    ],
    [
      "2772505322538799/3721",
      "179730609026279313065360/226981"
    ]
  ],
  "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=1507/2908.\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 [10,10]. The ten 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 2031996162762000342302590303680.\r\n",
  "created_at": "2026-11-03 18:01:01",
  "updated_at": "2026-11-03 18:01:01"
}