{
  "id": 4733,
  "curve_key": "0:648",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-1"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 12.947781392704549,
  "faltings_height": -0.8633623081496589,
  "conductor": "243",
  "bad_primes": [
    "3"
  ],
  "discriminant": "-243",
  "regulator": "0.5063673553800989597196501202430774640744",
  "points": [
    [
      "1",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 9 (Weierstrass model y^2 = x^3 - 432*9^2). Source: Elkies & Rogers, 'Elliptic Curves x^3+y^3=k of High Rank', ANTS-VI (LNCS 3076, 2004), arXiv:math/0403116, https://arxiv.org/abs/math/0403116.",
  "created_at": "2026-10-20 21:27:09",
  "updated_at": "2026-10-20 21:27:09"
}