{
  "id": 5567,
  "curve_key": "2800418253852997584288961:-4685086980488048165271184923221963041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-58342046955270783006020",
    "5422554375560008724410191466256400"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 168.87543304277636,
  "faltings_height": 11.800518975311443,
  "conductor": "16494598236522725424870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "37",
    "71",
    "73",
    "199",
    "359",
    "1721",
    "3271",
    "7129"
  ],
  "discriminant": "6828000822831565842775857621928590821564108248016044203038722560000",
  "regulator": "16109105.19441139918107524623784329715550568878214173",
  "points": [
    [
      "-268196905028",
      "42171452571959212"
    ],
    [
      "135487131640",
      "2250026250205180"
    ],
    [
      "153945842114920/1089",
      "9973142862911961980/35937"
    ],
    [
      "550729812899632/3721",
      "1238364682130621565676/226981"
    ],
    [
      "581282175340936/4225",
      "14015388124329173564/274625"
    ],
    [
      "603249508551400/8281",
      "29754763854327919618420/753571"
    ],
    [
      "14742121953625060/170569",
      "2256139056792230176025360/70444997"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (122191,1296480) 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 11:20:38",
  "updated_at": "2026-10-23 11:20:38"
}