{
  "id": 6126,
  "curve_key": "21300717582878611676101211100459680249544400:-98285855924489249361300889970770822816211046980260628146561672000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-443764949643304409918775231259576671865508",
    "113756777690381075649505886186659202715456527446363275538268988"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 299.30194400170456,
  "faltings_height": 22.66438086065363,
  "conductor": "120096546094927573418647101461067778384553568121916552400",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "29",
    "31",
    "47",
    "67",
    "79",
    "103",
    "181",
    "193",
    "277",
    "389",
    "3347",
    "4973",
    "10193",
    "82847",
    "85453",
    "1891367"
  ],
  "discriminant": "2583471425475989454749288341075684399458487180372264829147132295120007381789076890045089257083466209292333656552460100000000",
  "regulator": "8308438863222314.059214976492304781325919698427600300163438438220",
  "points": [
    [
      "121216524023914557919",
      "7857876394053858288137584902984"
    ],
    [
      "-672652634523615850683384443/1094116",
      "14211789669489244586927743645992245820417/1144445336"
    ],
    [
      "-2104885406214386819963/4",
      "113577459157810587367879642731375/8"
    ],
    [
      "6390918688269200868673/16",
      "30734521077367797509941602206775/64"
    ],
    [
      "49822903902592762541758/121",
      "1223127045932820308224448521779000/1331"
    ],
    [
      "244826293100491339689637/4",
      "121132720013938167073553750292271425/8"
    ],
    [
      "592791520545436121346418/3481",
      "1348716204515602630334518271298282000/205379"
    ],
    [
      "21824252962157705015211598/361201",
      "2026717383110737105489010076446855175000/217081801"
    ],
    [
      "7282176570556979578405309479/22231225",
      "197280008455787203107503327724204167651592/104820225875"
    ],
    [
      "27912292185265431967429647022/1138489",
      "4661595193463855188313652608662246659126000/1214767763"
    ],
    [
      "78071604486137175709538033323/98982601",
      "15707940563468265122441079976925581535301750/984777897349"
    ],
    [
      "5503499379785191384494005664142/15059462089",
      "1154142373452788072223748709791592158113073200/1848052009175813"
    ],
    [
      "167596626008021319613919888089593358/1105208814791761",
      "259678082565262663413222872910641775841374347780152200/36742314486140175873241"
    ]
  ],
  "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=74052/85453 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. An initial local PARI/GP effort0 replay seeded by its four selected sections returned bounds[13,13] but only twelve points, reproducing the source gap. One effort1 replay seeded by those twelve points recovered the thirteen displayed points with 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 03:19:13",
  "updated_at": "2026-10-29 03:19:13"
}