{
  "id": 5517,
  "curve_key": "198718594975485082576:-2797003268595260137605821034176",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-4139970728655939220",
    "3237272302994874661410568900"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 140.21526420671995,
  "faltings_height": 9.473795967832352,
  "conductor": "160175046391510920",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "61",
    "71",
    "139",
    "367",
    "2531"
  ],
  "discriminant": "13881485973490995458663648341006776289405836524100000000",
  "regulator": "369013.61920028175925681024946707623397636484678305",
  "points": [
    [
      "324302896",
      "43917826788990"
    ],
    [
      "1245283397",
      "3596488743582"
    ],
    [
      "18984173860",
      "2601253142405190"
    ],
    [
      "55193534740",
      "12958096035115350"
    ],
    [
      "40021947579040/44521",
      "146166971950767670650/9393931"
    ],
    [
      "1265750898354090/1413721",
      "26489096451230415695000/1680914269"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (8662,59675) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.",
  "created_at": "2026-10-22 21:22:21",
  "updated_at": "2026-10-22 21:22:21"
}