{
  "id": 4736,
  "curve_key": "0:3453192",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-3997"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 30.109619157298113,
  "faltings_height": 0.5667908388998049,
  "conductor": "1294947",
  "bad_primes": [
    "3",
    "73"
  ],
  "discriminant": "-6900772563",
  "regulator": "13.805737597671224689075985016522916911803109",
  "points": [
    [
      "73/4",
      "361/8"
    ],
    [
      "73",
      "620"
    ],
    [
      "3577/9",
      "213913/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 657 (Weierstrass model y^2 = x^3 - 432*657^2). 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 21:27:21",
  "updated_at": "2026-10-20 21:27:21"
}