{
  "id": 4729,
  "curve_key": "1546281890467297505404848:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-32214206051402031362601",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 167.0936865022852,
  "faltings_height": 11.992714286831923,
  "conductor": "1030854593644865003603232",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "41",
    "47",
    "79",
    "2441"
  ],
  "discriminant": "2139549165113804326253761711506788262837752357002901686727840407539264",
  "regulator": "5570514.5063738469453365023128372304021285868883089",
  "points": [
    [
      "180351302908",
      "7505950700076598"
    ],
    [
      "-55602865769759/400",
      "338653441212364798289/8000"
    ],
    [
      "34467728131900/9",
      "202135003390522396810/27"
    ],
    [
      "1300206430317942364/4223025",
      "1204603703661215826536940638/8678316375"
    ],
    [
      "-8411121412463/64",
      "22688786300873973049/512"
    ],
    [
      "5473196888023973988817/30160574224",
      "59732630606441533167527846372711/5237926604333632"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 179483163699. 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 21:26:30",
  "updated_at": "2026-10-20 21:26:30"
}