{
  "id": 4313,
  "curve_key": "1070456110528:-995335328339256320",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-22301168969",
    "1152015915597129"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 83.0973178352879,
  "faltings_height": 4.89925072354215,
  "conductor": "11684457043048128",
  "bad_primes": [
    "2",
    "3",
    "47",
    "89",
    "97",
    "479",
    "521",
    "601"
  ],
  "discriminant": "136526536390837002946133324304384",
  "regulator": "27365.08736289190538216106263785098613217051307410187",
  "points": [
    [
      "1140247/9",
      "512424620/27"
    ],
    [
      "-10000",
      "37067877"
    ],
    [
      "350600",
      "190863777"
    ],
    [
      "-163255",
      "-21015768"
    ],
    [
      "40208",
      "17897835"
    ],
    [
      "2719541/25",
      "456000336/125"
    ],
    [
      "235640",
      "94768713"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Volkan Dagli",
      "at": "2026-10-17 09:56:50"
    }
  ],
  "commentary": "Curve 2x2-7.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 09:49:54",
  "updated_at": "2026-10-17 09:56:50"
}