{
  "id": 4593,
  "curve_key": "3241827879570725403636648483529:-5831009146979494141265085843355889522928057733",
  "ainvs": [
    "1",
    "0",
    "1",
    "-67538080824390112575763510074",
    "6748853179374408887179706582485861189763116"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 210.76107036272495,
  "faltings_height": 15.33740896831268,
  "conductor": "91936250668693485040694250195331770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "29",
    "41",
    "43",
    "73",
    "101",
    "107",
    "443",
    "4793",
    "33941",
    "503711881"
  ],
  "discriminant": "40019592367262252343616815259828557179018457598565730257057187558353641049217401275200",
  "regulator": "199210531841.1040387537954730681615465841522363731488471725",
  "points": [
    [
      "110185704745216073/256",
      "31036721749900850323751763/4096"
    ],
    [
      "18218821702492396910/116281",
      "-4566052620006680941360821048/39651821"
    ],
    [
      "331316742348758",
      "4554256605405388339953"
    ],
    [
      "3127037760156867529142/8392609",
      "-140325320531958329634091905417096/24313388273"
    ],
    [
      "142521235750284122/289",
      "-47475202610558299011094011/4913"
    ],
    [
      "14990557472021154992173/56085121",
      "1172432844673907358969685266902297/420021471169"
    ],
    [
      "142066981626105612197/908209",
      "-93782241655772155813253048799/865523177"
    ],
    [
      "2955494854406019557318/7946761",
      "-128831323526349264043803753466008/22401919259"
    ],
    [
      "76073472201899258",
      "-20982021541818477937336587"
    ],
    [
      "448796484060241839284191793333/2831017943850721",
      "24365890261879737187731052761969957122989143/150630852185045849821231"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 61/382 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-10-18 16:19:14",
  "updated_at": "2026-10-18 16:19:14"
}