{
  "id": 6082,
  "curve_key": "665716900800015609408:-50381272524122683559461512414720",
  "ainvs": [
    "0",
    "0",
    "0",
    "-13869102100000325196",
    "58311658014030883749376750480"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 145.99434463788913,
  "faltings_height": 10.219597134633396,
  "conductor": "1056738254468057369589312",
  "bad_primes": [
    "2",
    "3",
    "23",
    "47",
    "59",
    "131",
    "347",
    "491",
    "11329",
    "113761"
  ],
  "discriminant": "-1298171803292146613206686492839395684712914189356048219242496",
  "regulator": "25166164.936434741884778183641842112708218391248323990300",
  "points": [
    [
      "1020657692",
      "212648335019856"
    ],
    [
      "-865782592",
      "263951344568268"
    ],
    [
      "-5042827363",
      "3391468798059"
    ],
    [
      "9264226578",
      "851431549111088"
    ],
    [
      "-2205212308",
      "-279592758315144"
    ],
    [
      "2401090793/4",
      "-1792476888726123/8"
    ],
    [
      "160275626684/25",
      "60324330731755248/125"
    ],
    [
      "-238392274699/49",
      "-35364684367619055/343"
    ],
    [
      "276111678770/49",
      "-136806346101479760/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original search by mpjunior92 (2026), public Yukon elliptic-rank challenge submission f9dcdb3a-2049-49d5-94bb-cc04dc429991. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/098b17019380774646df844473bf6a59f257e748/submission/board/4-9b.ec . The source used a Mestre-Nagao sieve in the Kubert Z/4 family y^2 + x*y - t*y = x^3 - t*x^2 with t=u/(D*s^2), (D,s,u)=(6,8648,-1316843833). The nine supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-9 F_5 reduction matrix at nine good primes.",
  "created_at": "2026-10-29 00:48:11",
  "updated_at": "2026-10-29 00:48:11"
}