{
  "id": 4719,
  "curve_key": "75480768:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1572516",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 54.41816535988087,
  "faltings_height": 2.603087524964896,
  "conductor": "25160256",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19"
  ],
  "discriminant": "248865785384491782144",
  "regulator": "22.688064423647360564945346115224478674797737",
  "points": [
    [
      "-912",
      "25992"
    ],
    [
      "1650",
      "43560"
    ],
    [
      "-528",
      "26136"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 1254. Source: Watkins, Donnelly, Elkies, Fisher, Granville, Rogers, 'Ranks of quadratic twists of elliptic curves', Publ. Math. Besancon 2014/2, 63-98, doi:10.5802/pmb.9 (https://pmb.centre-mersenne.org/item/10.5802/pmb.9.pdf), Table 2 'Smallest rank r quadratic twists y^2=x^3-d^2x'.",
  "created_at": "2026-10-20 21:25:49",
  "updated_at": "2026-10-20 21:25:49"
}