{
  "id": 4721,
  "curve_key": "2098312300150034781888:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-43714839586459057956",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 147.28626092368796,
  "faltings_height": 10.342095488615488,
  "conductor": "699437433383344927296",
  "bad_primes": [
    "2",
    "3",
    "17",
    "31",
    "449",
    "4657"
  ],
  "discriminant": "5346463929781116455900283179857035792614088511271306289844224",
  "regulator": "2680449.3325836379883504750827325607287798840076862",
  "points": [
    [
      "165541824817/16",
      "51806810701954601/64"
    ],
    [
      "271329342673/16",
      "130148817129300583/64"
    ],
    [
      "-156630507",
      "82723846945707"
    ],
    [
      "-204975397538/81",
      "224003566698561944/729"
    ],
    [
      "548503784857/36",
      "365985935192610019/216"
    ],
    [
      "2724841474883505553/404492544",
      "861524446768349238596781127/8135154044928"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 6611719866. 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 21:25:57",
  "updated_at": "2026-10-20 21:25:57"
}