{
  "id": 4716,
  "curve_key": "1200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-25",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 21.270230507328275,
  "faltings_height": -0.15924037941448668,
  "conductor": "800",
  "bad_primes": [
    "2",
    "5"
  ],
  "discriminant": "1000000",
  "regulator": "1.899482172531795590107205509594597919673",
  "points": [
    [
      "-4",
      "6"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 5. 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 21:25:40",
  "updated_at": "2026-10-20 21:25:40"
}