{
  "id": 4822,
  "curve_key": "0:46656",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-54"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 21.50111363073666,
  "faltings_height": -0.150584621646983,
  "conductor": "1728",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "-1259712",
  "regulator": "2.263730709543681793266213535376046073300",
  "points": [
    [
      "7",
      "17"
    ]
  ],
  "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+2, giving y^2=x^3-54. I recovered one rational point with PARI/GP and checked it exactly on this minimal model. PARI/GP returned matching rank bounds [1,1]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:57:54",
  "updated_at": "2026-10-20 21:57:54"
}