{
  "id": 6111,
  "curve_key": "106730586182839428926263162543052218422673296:-1093618417919587066908013670584346559724720458052511026140407665344",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2223553878809154769297149219646921217139027",
    "1265762057777299845958349155768919629311019048671887761736582946"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 304.1366450365915,
  "faltings_height": 23.201239710070222,
  "conductor": "1186882284700177882316018479268883158412782043090562882320",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "37",
    "43",
    "59",
    "61",
    "67",
    "79",
    "137",
    "149",
    "157",
    "229",
    "379",
    "727",
    "1223",
    "4007",
    "6353",
    "9029",
    "10067",
    "19753"
  ],
  "discriminant": "11464976536649803948573156066163467288936659656709853563142454478331178530805912010448621964490930420726396510696519398544000000",
  "regulator": "764924589652663.2622881500575513146030127023900958383977866674320",
  "points": [
    [
      "-1706958221957946655203",
      "9364859099692985257788047428800"
    ],
    [
      "68227195200517007422",
      "33382222925420533273583432940800"
    ],
    [
      "930415507505245499947",
      "1539040687934489748718610808050"
    ],
    [
      "-3465680755762116227442227/23409",
      "142891552746843916011395000421155336000/3581577"
    ],
    [
      "1539713008537589717745/4",
      "172860744164781963798593744381073/8"
    ],
    [
      "30664267002866482432737/121",
      "35678164277011709384403424377434100/1331"
    ],
    [
      "35102254537098355925937/121",
      "33806372883159695077252116753153300/1331"
    ],
    [
      "440292612963698445178107/841",
      "381864644657063267347071918001978470/24389"
    ],
    [
      "981593525476561157858577/841",
      "393656654717950097160017997283718100/24389"
    ],
    [
      "335499389949578668181610297/516961",
      "3642808777051665101594471934635339260380/371694959"
    ],
    [
      "235081196816485636977027767517/253414561",
      "4702491568603569724206279284964161060989200/4034106396559"
    ],
    [
      "1851693642215855090972783800411/1819790281",
      "584798621679459229103126173894272205652305190/77630433597179"
    ],
    [
      "3779563399716471421697488566873/3081693169",
      "3350173565432006735513341804692279315291301860/171074032890697"
    ]
  ],
  "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=35816/160175 in the rank-five X400a family posted by wgxli with curve#4252: y^2=x(x+A)(x+B), A=q(121p-99q)(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 02:38:10",
  "updated_at": "2026-10-29 02:38:10"
}