{
  "id": 6091,
  "curve_key": "36265575206326329098246837017763224972096:-6903228620433783284818412343342353228373958389132807850809856",
  "ainvs": [
    "0",
    "1",
    "0",
    "-755532816798465189546809104536733853585",
    "7989847940316878801621318162157864877065367322947023727983"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 280.1750627299645,
  "faltings_height": 21.091940735913873,
  "conductor": "38108330957491470085780912737156432881247314621760",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "41",
    "43",
    "59",
    "109",
    "151",
    "227",
    "233",
    "347",
    "353",
    "433",
    "521",
    "557",
    "641",
    "881",
    "1559",
    "19853",
    "21163"
  ],
  "discriminant": "24089703607477327530085267350902516670105832293822661623835593101403375582262831044117657277258523292630806784000000",
  "regulator": "2483526009262879.659396791636062717616695922318197712425270044923",
  "points": [
    [
      "14626753728175201711",
      "8254171010364237089079009600"
    ],
    [
      "-415882311129619850738093281529/14588049961",
      "140507163420169743941501249323794467525496000/1761959262339541"
    ],
    [
      "-3733046429655378075799646759/195748081",
      "340554610078172559047247374965799554322400/2738711401271"
    ],
    [
      "-1459222151614544636430923/63001",
      "1807398901162947657367443922382375820/15813251"
    ],
    [
      "-1224457679394774288569/121",
      "160820800292875452408138754467600/1331"
    ],
    [
      "-23781208640913292067/4",
      "886217039064514323433840895685/8"
    ],
    [
      "376713965734675424149/25",
      "644038817486951915528883820668/125"
    ],
    [
      "4903919969530161762917551/319225",
      "530442036865350620989149211231349376/180362125"
    ],
    [
      "7865780035255888092790471/516961",
      "1514647271101089323684193310845396000/371694959"
    ],
    [
      "4162620805916161678497025639/253032649",
      "14398135262044230410638327434764949585600/4024990347643"
    ],
    [
      "462952838247993543820678987021/24690961",
      "314995725237741793909701836074323547940955900/122689385209"
    ],
    [
      "220643690783808519056854517995831/14307011216521",
      "132079377906924966017803720552854888219936639600/54115711953053238181"
    ],
    [
      "139026952610292183613005797473855321/6479904820596736",
      "21227054333804738838321830758673503310483713179677475/521618445142101888598016"
    ]
  ],
  "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=4796/196149 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 02:06:24",
  "updated_at": "2026-10-29 02:06:24"
}