{
  "id": 3584,
  "curve_key": "6535087107856:-16702668844647196096",
  "ainvs": [
    "0",
    "1",
    "0",
    "-136147648080",
    "19331747261718228"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 88.5246203770519,
  "faltings_height": 5.096464354953698,
  "conductor": "12067267920",
  "bad_primes": [
    "2",
    "3",
    "5",
    "71",
    "73",
    "89",
    "109"
  ],
  "discriminant": "67820678763755950186411107225600",
  "regulator": "9242.847619273834077397377037014521771120668228",
  "points": [
    [
      "1033902843",
      "33244481732112"
    ],
    [
      "-2357526/49",
      "55062790560/343"
    ],
    [
      "5192447883/27889",
      "97393728124440/4657463"
    ],
    [
      "34491557841/160000",
      "18330671582361/64000000"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "Inspired by (much better) curve#3566\r\nSpecialized curve of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), where u±v=d*w^2. Here (u,v)=(-14418, 1278), with v-u=15696=109*12^2. PARI/GP gives exact rank 4 and torsion C2 x C4.",
  "created_at": "2026-09-28 21:40:06",
  "updated_at": "2026-09-28 21:40:06"
}