{
  "id": 4818,
  "curve_key": "0:2636064",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-3051"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 29.569594907041452,
  "faltings_height": 0.5217888180450829,
  "conductor": "1379052",
  "bad_primes": [
    "2",
    "3",
    "113"
  ],
  "discriminant": "-4021315632",
  "regulator": "14.660727178737668285219361376372018149499526",
  "points": [
    [
      "15",
      "18"
    ],
    [
      "51",
      "360"
    ],
    [
      "105/4",
      "981/8"
    ]
  ],
  "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+113, giving y^2=x^3-3051. I recovered three rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [3,3]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:54:23",
  "updated_at": "2026-10-20 21:54:23"
}