{
  "id": 6457,
  "curve_key": "2017499265178676928:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-42031234691222436",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 126.44517129249306,
  "faltings_height": 8.605338019349245,
  "conductor": "672499755059558976",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "19",
    "59",
    "163"
  ],
  "discriminant": "4752218684337266390160101855832733307054794676342784",
  "regulator": "22279.7946860881768229550972828595454132508145010",
  "points": [
    [
      "-203128563",
      "395491312161"
    ],
    [
      "-95856387",
      "1774314226377"
    ],
    [
      "-39138594",
      "1259003485080"
    ],
    [
      "611272332",
      "14237687237796"
    ],
    [
      "943474603938/1849",
      "839198807097608952/79507"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x, n = 205015206. Rank 5 example of Rogers, obtained at m/n = 18 in Family II, as recorded in Watkins, Donnelly, Elkies, Fisher, Granville and Rogers, Ranks of quadratic twists of elliptic curves (2014), section 12; https://www.dpmms.cam.ac.uk/~taf1000/papers/rankcongr.pdf. Witness points independently recomputed with PARI/GP ellrank (rank bounds [5,5]).",
  "created_at": "2026-11-03 18:31:19",
  "updated_at": "2026-11-03 18:31:19"
}