{
  "id": 5518,
  "curve_key": "29614442122746691921:-160957052040206776481403518969",
  "ainvs": [
    "1",
    "1",
    "1",
    "-616967544223889415",
    "186292884048725070093522372"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 134.50438147735778,
  "faltings_height": 8.990486474188073,
  "conductor": "40914952311895935",
  "bad_primes": [
    "3",
    "5",
    "7",
    "13",
    "19",
    "47",
    "61",
    "73",
    "83",
    "197",
    "461"
  ],
  "discriminant": "37698352886350825733869659528435365470643999351390625",
  "regulator": "9379.1687832597904616222739902573698927114057148925",
  "points": [
    [
      "-42763518",
      "14580775281971"
    ],
    [
      "6950129543/4",
      "528231464058483/8"
    ],
    [
      "-139766337767/169",
      "25135915689619487/2197"
    ],
    [
      "53215294697/121",
      "181252974124401/1331"
    ],
    [
      "254797267447/196",
      "109110539295483949/2744"
    ],
    [
      "115771628338933/374544",
      "1148826406833927326663/229220928"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (10244,74119) 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 21:22:26",
  "updated_at": "2026-10-22 21:22:26"
}