{
  "id": 3780,
  "curve_key": "251974086178753:-3890420874071335288385",
  "ainvs": [
    "1",
    "1",
    "1",
    "-5249460128724",
    "4502799750307510356"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 99.48104209658501,
  "faltings_height": 6.200687203760672,
  "conductor": "874968923829",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "83",
    "277"
  ],
  "discriminant": "499245970100099981317154927071636905009",
  "regulator": "68097.2092076381323085909473017801776941860633872",
  "points": [
    [
      "2154478",
      "1785976841"
    ],
    [
      "-42338306100/54289",
      "36055273588597524/12649337"
    ],
    [
      "253373109448/310249",
      "150618258172956751/172808693"
    ],
    [
      "1059889255247/68644",
      "1079621513283307545/17984728"
    ],
    [
      "275404626046/251001",
      "31722561133908584/125751501"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (4067,1196) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.",
  "created_at": "2026-10-01 19:48:37",
  "updated_at": "2026-10-01 19:48:37"
}