{
  "id": 4730,
  "curve_key": "2089586402823599881099968:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-43533050058824997522916",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 167.9970251545935,
  "faltings_height": 12.067992507857616,
  "conductor": "696528800941199960366656",
  "bad_primes": [
    "2",
    "17",
    "41",
    "103",
    "641",
    "2267"
  ],
  "discriminant": "5280040608225233465542032213204339387686129426586004579587920529362944",
  "regulator": "28669540.740131483585386386093918885123217944076883",
  "points": [
    [
      "-4455350155147/49",
      "19422836135704192827/343"
    ],
    [
      "664776050835949/81",
      "17134548249797036222255/729"
    ],
    [
      "433529065593702/121",
      "9011346481061668014336/1331"
    ],
    [
      "73932354598417/324",
      "257387620265847904679/5832"
    ],
    [
      "126918167055713017/125316",
      "44245436258381779900899091/44361864"
    ],
    [
      "24191462379842870240773569009457/104760622353480814224",
      "50986618599036294312283435416075741312135834409/1072252591811650831161964813632"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 208645752554. 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 21:26:34",
  "updated_at": "2026-10-20 21:26:34"
}