{
  "id": 4820,
  "curve_key": "0:-256608",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "297"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 24.910609815213512,
  "faltings_height": 0.13354006039275454,
  "conductor": "13068",
  "bad_primes": [
    "2",
    "3",
    "11"
  ],
  "discriminant": "-38106288",
  "regulator": "0.404128771490454734203976327400265637271859",
  "points": [
    [
      "-6",
      "9"
    ],
    [
      "12",
      "45"
    ]
  ],
  "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^3-11, giving y^2=x^3+297. I recovered two rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [2,2]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:55:26",
  "updated_at": "2026-10-20 21:55:26"
}