{
  "id": 4713,
  "curve_key": "0:-93236184",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "107912"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 36.70129288930677,
  "faltings_height": 1.1160969832338596,
  "conductor": "1294947",
  "bad_primes": [
    "3",
    "73"
  ],
  "discriminant": "-5030663198427",
  "regulator": "41.417212793013674067227955049568750735409326",
  "points": [
    [
      "-36",
      "247"
    ],
    [
      "-119/4",
      "2281/8"
    ],
    [
      "-18",
      "319"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Elkies and Rogers (2004), Elliptic Curves x^3+y^3=k of High Rank: https://arxiv.org/abs/math/0403116. This is the rational 3-isogenous partner of the cube-sum curve with k=657. I recovered three rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [3,3]. Rational torsion Z/3Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:18:56",
  "updated_at": "2026-10-20 21:18:56"
}