{
  "id": 4727,
  "curve_key": "804333722601845495627568:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-16756952554205114492241",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 165.1329036413878,
  "faltings_height": 11.829315715090473,
  "conductor": "536222481734563663751712",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "37",
    "61",
    "71",
    "269"
  ],
  "discriminant": "301137675666469835854802414497033408718907851837883666656813795425344",
  "regulator": "1479717.7595592296353982910608390093202624199254129",
  "points": [
    [
      "-1144374670439/16",
      "1846740346294288445/64"
    ],
    [
      "12463643091900",
      "43999129162103505390"
    ],
    [
      "-82686378852",
      "28639865139644682"
    ],
    [
      "-92901152548976772/1324801",
      "43936729597125810198655902/1524845951"
    ],
    [
      "-875516686641168/16129",
      "56084494263053852586276/2048383"
    ],
    [
      "288728101140297/1936",
      "2436279053497332857541/85184"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 129448648329. 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 21:26:22",
  "updated_at": "2026-10-20 21:26:22"
}