{
  "id": 6092,
  "curve_key": "80362813572228175672775746892722045417873:-15587455229172815388365210368448737388892293199736211032656985",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1674225282754753659849494726931709279539",
    "18041036144875943736394289523252772135860103679857786995984"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 282.56211053460004,
  "faltings_height": 21.57766315193356,
  "conductor": "39859666157079499691041689625437974568946385526573501",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "53",
    "59",
    "61",
    "107",
    "113",
    "157",
    "191",
    "337",
    "373",
    "541",
    "547",
    "877",
    "953",
    "1153",
    "2113",
    "7723",
    "25889"
  ],
  "discriminant": "159738946706579269556920638454117054758678150066292594269751017174036560949153635822058734073395179557481939933625651289",
  "regulator": "27819315179316.51292966624380944017979508662865020472755917302668",
  "points": [
    [
      "-44934311048500854945",
      "50444760890894982170526528543"
    ],
    [
      "-41343846407295598416",
      "128803527410077979391135510432"
    ],
    [
      "-1611847553655204115",
      "143998070843880432776030591282"
    ],
    [
      "259676734365180838707/4",
      "3421846263819753622727287336923/8"
    ],
    [
      "74957647499829361017",
      "560094414002426793485569082634"
    ],
    [
      "99236943747094801167",
      "910592433761113113189518216079"
    ],
    [
      "188033269603168189665",
      "2520204604506345671449125427962"
    ],
    [
      "-30519944076497489860739715/1697809",
      "455143618335686975336737920176005364199/2212245127"
    ],
    [
      "-47120265944688624409728/2209",
      "21789995731097739293318984060445108/103823"
    ],
    [
      "921940693413438966453/16",
      "21502952632620030452646873508029/64"
    ],
    [
      "119331197357438555238333/10201",
      "7761733799385233794261927727950266/1030301"
    ],
    [
      "54855113701106027350120689/5248681",
      "493586429371359637107736453711019539662/12024728171"
    ],
    [
      "67772720954835365230994068236/1539228289",
      "10404474541384341971025670955655687978603654/60388543462337"
    ]
  ],
  "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 rank13 at T=154352/100399 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 thirteen displayed points and bounds[13,13]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-13 F_5 reduction matrix at thirteen good primes.",
  "created_at": "2026-10-29 02:11:23",
  "updated_at": "2026-10-29 02:11:23"
}