{
  "id": 4725,
  "curve_key": "682267261486752812828208:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-14213901280974016933921",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 164.6391252389002,
  "faltings_height": 11.788167514883172,
  "conductor": "454844840991168541885472",
  "bad_primes": [
    "2",
    "3769",
    "4729",
    "6689"
  ],
  "discriminant": "183789145461521004412264716742066272272186125689814156724395698493504",
  "regulator": "496564848.84941929247945559856220755927643431822681",
  "points": [
    [
      "-225520462105552400/23319241",
      "1315922980592574487742406180/112608614789"
    ],
    [
      "-12537096713597551937600/34350019870321",
      "458543026396658098453521181462375560/201321653607745775369"
    ],
    [
      "253970200287659581174225/173652224656",
      "127563474012836868951204080308919655/72363660449749696"
    ],
    [
      "-265172088033772653963536/2374758050625",
      "51088291776632228802035470973705188/3659561524964390625"
    ],
    [
      "-61229933977612921062400/6920524614721",
      "203600278309385746546935850666810080/18205747978175772769"
    ],
    [
      "-4449186201994833087171326864/38819837726525025",
      "85023859702434342114580582724998796763116/7648575771762097995812625"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 119222067089. Source: Watkins et al. electronic data http://magma.maths.usyd.edu.au/~watkins/PTS.r6r7 (paper Sec. 15); 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).",
  "created_at": "2026-10-20 21:26:13",
  "updated_at": "2026-10-20 21:26:13"
}