{
  "id": 4720,
  "curve_key": "111850034787509808:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2330209058073121",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 117.76780618159826,
  "faltings_height": 7.8822242601080115,
  "conductor": "74566689858339872",
  "bad_primes": [
    "2",
    "23",
    "31",
    "79",
    "857"
  ],
  "discriminant": "809775498984225888766576997151308626762825635904",
  "regulator": "235509.867956499719913784565167724758784039657111",
  "points": [
    [
      "1004028775/9",
      "28681487598160/27"
    ],
    [
      "98138033",
      "846458786712"
    ],
    [
      "-19513711",
      "195039737760"
    ],
    [
      "483891794847/7921",
      "206295102244711416/704969"
    ],
    [
      "-21616933609/1369",
      "9181708658384880/50653"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 48272239. 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 21:25:53",
  "updated_at": "2026-10-20 21:25:53"
}