{
  "id": 4724,
  "curve_key": "431596069731839678607408:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-8991584786079993304321",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 163.26533123982833,
  "faltings_height": 11.673684681627185,
  "conductor": "287730713154559785738272",
  "bad_primes": [
    "2",
    "17",
    "73",
    "233",
    "353",
    "929"
  ],
  "discriminant": "46525248924722667505609765024253197486891774904954256748976221962304",
  "regulator": "6233794.1792463893888271373397276061326193775530017",
  "points": [
    [
      "106838034129793/1024",
      "460631008932227091777/32768"
    ],
    [
      "-1628386957963069696/17783089",
      "558916910302732383796593360/74991286313"
    ],
    [
      "-46486845596672/106929",
      "69131200965695619298912/34965783"
    ],
    [
      "1742541606737/16",
      "1131406526584434471/64"
    ],
    [
      "-40108757676814224/429025",
      "1362741020641041904891476/281011375"
    ],
    [
      "-15458376118106686464/169026001",
      "16646660409557056403887726560/2197507039001"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 94823967361. 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 21:26:10",
  "updated_at": "2026-10-20 21:26:10"
}