{
  "id": 6118,
  "curve_key": "6110160808634438015842740636875032513:-15077039774422901784930441181903495118970747809675673665",
  "ainvs": [
    "1",
    "1",
    "1",
    "-127295016846550791996723763268229844",
    "17450277516693173309148420274473622685359019714251076"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 254.10904931864476,
  "faltings_height": 18.970151157900364,
  "conductor": "2517462282771642323766182698181384519891875671381",
  "bad_primes": [
    "3",
    "7",
    "11",
    "29",
    "37",
    "43",
    "53",
    "73",
    "101",
    "103",
    "109",
    "257",
    "293",
    "383",
    "509",
    "797",
    "1567",
    "2459",
    "8821",
    "47521"
  ],
  "discriminant": "462970536193400224696922612913682692054850013767544734805815794000063526507277861420766606438953569667649",
  "regulator": "69662985163567.170662227224802485374066342833615007321805893570",
  "points": [
    [
      "-63299254815556292",
      "158916110119092803436992991"
    ],
    [
      "172246695613895139",
      "25189395381022336205935690"
    ],
    [
      "220383699928661639",
      "10017044195410449267485520"
    ],
    [
      "243556476413036807",
      "29907570735512959880996472"
    ],
    [
      "-1842783552974198739/16",
      "11192420285362737063642920851/64"
    ],
    [
      "548208354408854105/64",
      "65489039191130580798003928599/512"
    ],
    [
      "114238777978325214898/961",
      "1883664259056947035244389521736/29791"
    ],
    [
      "3337445805128832959348/17161",
      "15845008863041831626370050165836/2248091"
    ],
    [
      "7144727198984075070592/32041",
      "70889294470652480414670294517308/5735339"
    ],
    [
      "3492419230219663608011027/24433249",
      "5633076901696138009843281362716587330/120773549807"
    ],
    [
      "1003195428303300658151808386/4641560641",
      "1842525532153999144035015348282367728741/316224884910689"
    ],
    [
      "294765203207024731492186656073/1122362261056",
      "54922048055516246217803964378445499466539361/1189048537158903296"
    ]
  ],
  "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=2929/57979 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 03:06:20",
  "updated_at": "2026-10-29 03:06:20"
}