{
  "id": 6242,
  "curve_key": "1158571320043628161657441:-1218944969604839721106598218271245585",
  "ainvs": [
    "1",
    "0",
    "0",
    "-24136902500908920034530",
    "1410815937040627157553857379662916"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 166.22768957176586,
  "faltings_height": 11.753924497191921,
  "conductor": "165833851234486775281739639418068527351978197028047383177658",
  "bad_primes": [
    "2",
    "3",
    "1533109",
    "3217741",
    "95524043",
    "64377117305383",
    "911073883732752768320363"
  ],
  "discriminant": "40109355342009178495432474492917876619702110438642360030238831583232",
  "regulator": "1666174659472690105.212198130148132984965205055091465990867481679285630243545",
  "points": [
    [
      "3099001434872897801418522/746497728001",
      "5451707054137311802716965411290415394/644974783490592001"
    ],
    [
      "1313790581472",
      "-1495782243243778386"
    ],
    [
      "335453497980",
      "-176245084751722194"
    ],
    [
      "277646858466",
      "-126935004706920894"
    ],
    [
      "41101721646",
      "-22094882964608574"
    ],
    [
      "-13201439778",
      "-41559072806204286"
    ],
    [
      "-31884975882",
      "-46346554336533726"
    ],
    [
      "-153422073930",
      "38764103162250786"
    ],
    [
      "-157963890540",
      "35804640888986766"
    ],
    [
      "3604114549350564/58081",
      "172564281213416845007406/13997521"
    ],
    [
      "-19304816946972/121",
      "46119554630933821194/1331"
    ],
    [
      "-106806010264945356/779689",
      "31898277491622003292525386/688465387"
    ],
    [
      "139833643532654166/546121",
      "44242353597575046541410582/403583419"
    ],
    [
      "-83415444296664/625",
      "741959325039508724634/15625"
    ],
    [
      "659027954383812/4489",
      "9659480635710026828922/300763"
    ],
    [
      "120942684708",
      "16145492500321998"
    ],
    [
      "173222787176258364/1723969",
      "-132704905130230552012434/2263571297"
    ],
    [
      "26170244723025/256",
      "14001551263212858609/4096"
    ],
    [
      "17593963476",
      "31489645445621646"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original search by 0xArion (2026), public Yukon elliptic-rank challenge submission 598e1604-cd20-4fe0-ac6a-98105a476e90, validated 2026-10-31. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/ab6a5c670a3d01d0ddcfb34c37f09b98852d387a/submission/board/own-ec-r19-b3178d0fc424.ec . The nineteen supplied points were checked exactly on the displayed global minimal model and certified independent modulo torsion by an exact rank-19 F_3 reduction matrix at 21 good primes. They are not 2-saturated (the F_2 matrix has rank 18), so the certificate uses F_3. The rational torsion subgroup is trivial (the gcd of #E(F_p) over good primes p >= 5 is 1). The complete bad-prime list was verified from the minimal discriminant, with every large factor proved prime.",
  "created_at": "2026-10-31 20:38:20",
  "updated_at": "2026-10-31 20:38:20"
}