{
  "id": 4777,
  "curve_key": "0:31692394368",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-36681012"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 48.35868512748657,
  "faltings_height": 2.087546336415509,
  "conductor": "49833208938672",
  "bad_primes": [
    "2",
    "3",
    "113213"
  ],
  "discriminant": "-581254549060670208",
  "regulator": "5949.3459158112009516773871142764891323717318315581",
  "points": [
    [
      "333",
      "495"
    ],
    [
      "486",
      "8838"
    ],
    [
      "702",
      "17586"
    ],
    [
      "981",
      "30123"
    ],
    [
      "1021",
      "32057"
    ],
    [
      "2133",
      "98325"
    ]
  ],
  "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+1358556, giving y^2=x^3-36681012. I recovered six rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [6,6]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:31:15",
  "updated_at": "2026-10-20 21:31:15"
}