{
  "id": 4857,
  "curve_key": "0:48732192",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-56403"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 35.4037007927299,
  "faltings_height": 1.0079643085191203,
  "conductor": "157101156",
  "bad_primes": [
    "2",
    "3",
    "2089"
  ],
  "discriminant": "-1374320912688",
  "regulator": "158.0880548393265226661240019500386563426014024",
  "points": [
    [
      "39",
      "54"
    ],
    [
      "43",
      "152"
    ],
    [
      "103",
      "1018"
    ],
    [
      "363",
      "6912"
    ]
  ],
  "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+2089, giving y^2=x^3-56403. I recovered four rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [4,4]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:09:32",
  "updated_at": "2026-10-20 22:09:32"
}