{
  "id": 6112,
  "curve_key": "30215003815598369543903034743367024:-5220466205681610267107790934428104581102891907932032",
  "ainvs": [
    "0",
    "0",
    "0",
    "-629479246158299365497979890486813",
    "6042206256575937809152535803736232154054273041588"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 238.18094005469584,
  "faltings_height": 17.69199757554521,
  "conductor": "23703601279261618408300123405376197309751759520",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "31",
    "41",
    "73",
    "103",
    "131",
    "193",
    "251",
    "353",
    "373",
    "467",
    "499",
    "601",
    "2963",
    "3449",
    "9887"
  ],
  "discriminant": "191790065984348206679942395675989918474526281725783273415493925766393702313133190813854480360193600",
  "regulator": "3281895421036.9372111279349860827521899870323450620445989372621",
  "points": [
    [
      "3657326156421429",
      "1946513772348233844820680"
    ],
    [
      "17609977543593069",
      "646640593054981734894300"
    ],
    [
      "194559402035973444",
      "85136938906052505814590600"
    ],
    [
      "287735706873371389/9",
      "116429892992067439483300448/27"
    ],
    [
      "761443006037519901/49",
      "38874620322733006917652140/343"
    ],
    [
      "1637583600083881389/121",
      "57489200670962879516422800/1331"
    ],
    [
      "16967409482962323039/361",
      "61458509687248115217332065080/6859"
    ],
    [
      "22705213988280302244/841",
      "72044459142777290617193552400/24389"
    ],
    [
      "157473041151696163341/85849",
      "55644537654683109057733439108400/25153757"
    ],
    [
      "233324686248267836239/28561",
      "5802178045354771946265696286180/4826809"
    ],
    [
      "6121111262553181007929/456976",
      "36236461823514714247283758731155/308915776"
    ],
    [
      "3972506521099255035878421817812277/254867031180032041",
      "16974827458755102943979858112012251264573829144740/128667982151095719472858411"
    ]
  ],
  "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=34091/10217 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 02:43:05",
  "updated_at": "2026-10-29 02:43:05"
}