{
  "id": 5996,
  "curve_key": "2467347075498938915263337521:-156534499800574092139616888506021470784681",
  "ainvs": [
    "1",
    "0",
    "0",
    "-51403064072894560734652865",
    "181174189583993508239587546409315481225"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 189.7081901169268,
  "faltings_height": 13.819070257131495,
  "conductor": "13248616279429857526445142990382290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "37",
    "43",
    "53",
    "73",
    "113",
    "8039",
    "7172542378144321"
  ],
  "discriminant": "-5487459592656539598234556515135205131426620429422979609850314651489088000000000",
  "regulator": "2365993945540.24049752898635012123959560785193135532960163275",
  "points": [
    [
      "87062806349166744010/24039409",
      "-768503751152504026624201931075/117865222327"
    ],
    [
      "-17568678489248604673880/2463434689",
      "-1663157548796893782648621080910605/122267653919137"
    ],
    [
      "1487187171265288630/337561",
      "1243844093748788865637193735/196122941"
    ],
    [
      "36626410903347177253018/3490091929",
      "-5822661043353338635701436563982337/206184160889533"
    ],
    [
      "6920649291580",
      "12525921019892422585"
    ],
    [
      "232387829516603116/121",
      "-112025542027932350086907503/1331"
    ],
    [
      "6938830659422170/2209",
      "739277395813920793720805/103823"
    ],
    [
      "184042956228442330/22201",
      "59611240765015457883694415/3307949"
    ],
    [
      "42533172040655728330/9928801",
      "196840083497747150011148142085/31285651951"
    ],
    [
      "372005096860330",
      "-7173703760385277814165"
    ],
    [
      "3464957170961935498/49729",
      "-6417308831026743875780313803/11089567"
    ]
  ],
  "submitter": "Mahesh Panchpor",
  "history": [],
  "commentary": "t = 1565/17\r\n\r\nFamily y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3 (Z/3Z K3 family, parameter t=1565/17). Family construction from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-r12-z3k3.ec (commit c8f82607a219df846ab80dd9e14ee09a2904d709, 2026-10-17). Not itself a repository curve: this t-value is not in that file.",
  "created_at": "2026-10-27 17:43:11",
  "updated_at": "2026-10-27 17:43:11"
}