{
  "id": 6096,
  "curve_key": "6408056389989444296054326212211251645123136:-13247362711889953233825181157908409907605163727875655121934255616",
  "ainvs": [
    "0",
    "1",
    "0",
    "-133501174791446756167798462754401075940065",
    "15332595731354112539105014837463510696561154827086096773221663"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 295.69838974623957,
  "faltings_height": 22.645826949448242,
  "conductor": "172693048172172746400478624258257772692731498377790306880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "31",
    "41",
    "43",
    "59",
    "73",
    "131",
    "211",
    "331",
    "479",
    "659",
    "2447",
    "3593",
    "3769",
    "4721",
    "24469",
    "57737"
  ],
  "discriminant": "50719095537321448486800593157100404934230977199779466030406948057247732050876048362567274754770441269937704153912075264000000",
  "regulator": "445317368017876.8655270644879605820556204719686065986455254220463",
  "points": [
    [
      "-330283774209081176209",
      "4836949330242889465120675611360"
    ],
    [
      "128903579514384143471",
      "515456524321435476243858794400"
    ],
    [
      "331570117565544088961",
      "2742261367287858543362131795080"
    ],
    [
      "511309597216888250783",
      "8985970665084869074186730049888"
    ],
    [
      "572414222952040519871",
      "11245921410467874953108759054400"
    ],
    [
      "736970563116866485871",
      "17810495419198384855528263626400"
    ],
    [
      "-577984271452349146883593129/1819801",
      "12443979105891650904095682740785162744800/2454911549"
    ],
    [
      "-173863889526224766295340569/1413721",
      "9189988924108047777441261100034611873920/1680914269"
    ],
    [
      "-31615638174476359771507969/192721",
      "484676964432577689134706955960181838720/84604519"
    ],
    [
      "4073048705057645142562/9",
      "186289891113480928064364431532889/27"
    ],
    [
      "165120132157853634795161/256",
      "57571904728770442402488373808899005/4096"
    ],
    [
      "516277535192655563386877450599/1287159129",
      "236888155140465681055434722864336622478106560/46179408071133"
    ],
    [
      "59828651045744227502539841125151/455367186481",
      "75565020487319621516801951621428649325034651200/307285875742057129"
    ]
  ],
  "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=11017/30600 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_7 reduction matrix at thirteen good primes.",
  "created_at": "2026-10-29 02:22:48",
  "updated_at": "2026-10-29 02:22:48"
}