{
  "id": 5556,
  "curve_key": "3159813518211467341337296:-5489215261887074616043467848003249344",
  "ainvs": [
    "0",
    "1",
    "0",
    "-65829448296072236277860",
    "6353258404939948767284952597170400"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 169.23766573347106,
  "faltings_height": 12.005132199626246,
  "conductor": "220660066076915225659080",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "29",
    "47",
    "53",
    "61",
    "79",
    "271",
    "751",
    "883"
  ],
  "discriminant": "820269525861198707613359536251388337280652370830493155680416057760000",
  "regulator": "119568.8967570378474780012248365695725581342802170361",
  "points": [
    [
      "-293671201125",
      "18932839667644980"
    ],
    [
      "172778563870",
      "11713292448448890"
    ],
    [
      "19998251709595",
      "89423666410417846260"
    ],
    [
      "-1084401308150/81",
      "61995704294812739230/729"
    ],
    [
      "775570849117/4",
      "237140995426403757/8"
    ],
    [
      "16331164423432/9",
      "65369606701332450608/27"
    ],
    [
      "123183662565430/121",
      "1327307430164493154650/1331"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (191055,679354) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.",
  "created_at": "2026-10-23 02:45:46",
  "updated_at": "2026-10-23 02:45:46"
}