{
  "id": 6115,
  "curve_key": "99500356347441505736233782669049408:-31073348891885830908759075377381819692585323548546560",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2072924090571698036171537138938529",
    "35964524180423414712681640385107390364794707794271"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 241.75640788302888,
  "faltings_height": 18.011388114189884,
  "conductor": "977582092190237829070067009190555061574831808",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "19",
    "53",
    "59",
    "83",
    "101",
    "107",
    "113",
    "127",
    "131",
    "263",
    "541",
    "653",
    "1949",
    "3221",
    "4721",
    "129061"
  ],
  "discriminant": "11303499691733521737850035966749094517714554982954090728765321160814027894475538035382762336255279104",
  "regulator": "39598077723446.514568519932382123032217947776972603561041753247",
  "points": [
    [
      "-46999446370778027",
      "5437966316885264379585060"
    ],
    [
      "10380718040479474",
      "3945212625380131467544875"
    ],
    [
      "113020952208516277",
      "35289948068652460905115380"
    ],
    [
      "451006563891795775",
      "301394954366595962249341536"
    ],
    [
      "-3790030437584244160003481/87254281",
      "5409557508130450140149818167246701280/815042238821"
    ],
    [
      "-38220317764658385047/3136",
      "1353704119935528125442364424235/175616"
    ],
    [
      "835619932553601/16",
      "383232637433418846653711703/64"
    ],
    [
      "1309781876686790521/25",
      "1054509321698772586705704744/125"
    ],
    [
      "4137656608551344575/49",
      "7380732736162855067926388448/343"
    ],
    [
      "210136272591919518415/5329",
      "1533469411088830786273426937472/389017"
    ],
    [
      "137876030608667166668863/2362369",
      "38731410202568556912025946202946080/3630961153"
    ],
    [
      "4695054606190088966523081/301473769",
      "14295720872454252294474874042754486520/5234489051147"
    ]
  ],
  "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=51931/81150 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_7 reduction matrix at twelve good primes.",
  "created_at": "2026-10-29 02:53:49",
  "updated_at": "2026-10-29 02:53:49"
}