{
  "id": 4783,
  "curve_key": "0:-659692512",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "763533"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 40.61456878702953,
  "faltings_height": 1.4422033080440895,
  "conductor": "28789266276",
  "bad_primes": [
    "2",
    "3",
    "28279"
  ],
  "discriminant": "-251848501382448",
  "regulator": "762.206551932620889636041336233270786257568014086",
  "points": [
    [
      "-53",
      "784"
    ],
    [
      "7",
      "874"
    ],
    [
      "123",
      "1620"
    ],
    [
      "231",
      "3618"
    ],
    [
      "33/4",
      "6993/8"
    ]
  ],
  "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^3-28279, giving y^2=x^3+763533. I recovered five rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [5,5]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:34:13",
  "updated_at": "2026-10-20 21:34:13"
}