{
  "id": 4810,
  "curve_key": "0:-58809036807936",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "68066014824"
  ],
  "rank_lower_bound": 8,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 63.41063329246851,
  "faltings_height": 3.341875350164005,
  "conductor": "57197313259518367296",
  "bad_primes": [
    "2",
    "3",
    "311",
    "1013249"
  ],
  "discriminant": "-2001448385577066708421632",
  "regulator": "902205.665137568961284890186175520908920124522039126087",
  "points": [
    [
      "-3050",
      "199232"
    ],
    [
      "-95",
      "260893"
    ],
    [
      "1210",
      "264268"
    ],
    [
      "1353",
      "265599"
    ],
    [
      "2838",
      "301536"
    ],
    [
      "6726",
      "610200"
    ],
    [
      "8265",
      "795393"
    ],
    [
      "13530",
      "1595268"
    ]
  ],
  "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^3-2520963512, giving y^2=x^3+68066014824. I recovered eight rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [8,8]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:42:51",
  "updated_at": "2026-10-20 21:42:51"
}