{
  "id": 6119,
  "curve_key": "1255819695679377543312455766932638521:-1399612512224644070628592388510947670833270102176345069",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-26162910326653698819009495144429969",
    "1619921889148893606805302105402947471920510478441225"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 249.362555553394,
  "faltings_height": 18.61979035606875,
  "conductor": "6372814782902779568050252265518228012820488033770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "31",
    "37",
    "41",
    "43",
    "53",
    "71",
    "103",
    "173",
    "181",
    "223",
    "239",
    "313",
    "461",
    "677",
    "3361",
    "7001",
    "27647"
  ],
  "discriminant": "12509747942419163659993416753354658681701179718184007262176745415856042279249361874377847277423683522500",
  "regulator": "150689135619.65833158299943785914990258765921238144906856039253",
  "points": [
    [
      "-132949822306730204",
      "52424240101757686679982697"
    ],
    [
      "29058304948404049",
      "29735642939271256826818744"
    ],
    [
      "38902405976566175",
      "25709852605794879685936680"
    ],
    [
      "68486477919995191",
      "12220684249892278317449992"
    ],
    [
      "87686638217831566",
      "45918972655195128918817"
    ],
    [
      "99625484933114326",
      "1495270667617091119015597"
    ],
    [
      "114174340377956176",
      "11006381870339813300976397"
    ],
    [
      "130181060231320024",
      "20498756703226525400131219"
    ],
    [
      "-580372782000915733436/5929",
      "25998303245515766854657399578461/456533"
    ],
    [
      "-104656837510524386231/1849",
      "4295918448674154584576048370709/79507"
    ],
    [
      "-1524415693989731354/9",
      "932177689056560691383119159/27"
    ],
    [
      "24842619046314373129/64",
      "114429894231732613938747064169/512"
    ]
  ],
  "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=77011/124357 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 03:10:10",
  "updated_at": "2026-10-29 03:10:10"
}