{
  "id": 4838,
  "curve_key": "0:23328",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-27"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 20.11481926961677,
  "faltings_height": -0.2661091517403072,
  "conductor": "36",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "-314928",
  "regulator": "1",
  "points": [],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.3: https://johncremona.github.io/theses/womack.pdf. This is the rational 3-isogenous partner of the Mordell curve y^2=x^3+1, giving y^2=x^3-27. I checked this minimal model with PARI/GP, which returned matching rank bounds [0,0]. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:02:27",
  "updated_at": "2026-10-20 22:02:27"
}