{
  "id": 6113,
  "curve_key": "32358298522540638512910960719610688:-5780424518740743089476868006508162447863979400133120",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-674131219219596635685645014991889",
    "6690306155949934356049374006657399913576092265969"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 238.3865357398857,
  "faltings_height": 17.714989341886568,
  "conductor": "4839954604749099000664203083594381012438592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "43",
    "73",
    "257",
    "431",
    "1741",
    "7333",
    "9067",
    "16381",
    "154571"
  ],
  "discriminant": "270691963989245919978429504052914521480886396206053429237856658080489271792280692477131799566106624",
  "regulator": "1509389547620.0282644854206329413212052896724466657671155167623",
  "points": [
    [
      "-20748726704338541",
      "3427118806018673508164604"
    ],
    [
      "-19129718467060928",
      "3547647132212205772654905"
    ],
    [
      "11899297211284405",
      "594540890900446294849968"
    ],
    [
      "43620668554081893",
      "7764279351574274401032160"
    ],
    [
      "-21694207514283076499/729",
      "12410365864046470344047742992/19683"
    ],
    [
      "-602648564109378547/121",
      "4193033113001488374257299920/1331"
    ],
    [
      "-6863841667612275/4",
      "22402908331055395362233329/8"
    ],
    [
      "146342796461497099/9",
      "4510850607405331847517860/27"
    ],
    [
      "1307920290533817616/81",
      "89472677579257461788414665/729"
    ],
    [
      "1598054712882320536/25",
      "1874113864646113362349686609/125"
    ],
    [
      "3676823001542245381/225",
      "656976047343129283945704704/3375"
    ],
    [
      "3921490511007834831220873618252525/422778782872934569",
      "305545469095755800904092322455297547862346948844864/274896858134579604369742997"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source parameter/search by bufferhe4d (2026), public Yukon submission 15009775-297e-4a19-9179-4a455b778310: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/6837b3bcd53a73fb5af3e271d91dec3148236631/submission/search/x400a-opus/xlog.txt . The source log records rank12 at T=1364/12167 in the rank-five X400a family posted by wgxli with curve#4252: y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q). The published section code credits 0xArion submission7e9f6673-cf5f-4cb9-82b4-a22add86d720. Using its four selected sections, a local seeded PARI/GP replay recovered the twelve displayed points and bounds[12,12]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-12 F_5 reduction matrix at twelve good primes.",
  "created_at": "2026-10-29 02:46:15",
  "updated_at": "2026-10-29 02:46:15"
}