{
  "id": 5579,
  "curve_key": "645588913:-3985881888745",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13449769",
    "4612168409"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 60.85702050480093,
  "faltings_height": 3.1359705329002368,
  "conductor": "13324206",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "59",
    "283"
  ],
  "discriminant": "146518836492786321441024",
  "regulator": "15.086174744939631632395779602679352282184308",
  "points": [
    [
      "-3700",
      "62897"
    ],
    [
      "-3616",
      "79067"
    ],
    [
      "-3430",
      "103667"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Specialization at (u,v) = (112,171) of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), giving y^2 = x(x+12544)(x+29241). Found in my own run scanning coprime positive integer pairs u < v, with v <= 250. The displayed global minimal model [1,0,0,-13449769,4612168409] is obtained by x = 4X - 13928, y = 8Y + 4X. Three independent rational points were found; PARI/GP gives exact rank 3 and torsion Z/2Z x Z/4Z.",
  "created_at": "2026-10-23 19:10:56",
  "updated_at": "2026-10-23 19:10:56"
}