{
  "id": 3566,
  "curve_key": "18287474505377296:-2472591380702506696350656",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-380989052195360",
    "2861795706513140889600"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 112.33497830146476,
  "faltings_height": 7.07566002188536,
  "conductor": "3250497013680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "37",
    "71",
    "109",
    "233"
  ],
  "discriminant": "1275165844926449727808127025206841600000000",
  "regulator": "68593.2459687626429232906235691166725351656011182",
  "points": [
    [
      "11131802",
      "347236722"
    ],
    [
      "-47655300097680/2217121",
      "110506559938170270000/3301293169"
    ],
    [
      "96966505/9",
      "74696217400/27"
    ],
    [
      "654597680/49",
      "4287766935600/343"
    ],
    [
      "55517508080/5329",
      "1880467759371600/389017"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found in a targeted low-conductor search in the C2 x C4 family y^2 = x(x+u^2)(x+v^2), using low-squarefree-kernel loci u±v=d*w^2. Here (u,v)=(497,5825), with v-u=5328=37*12^2. PARI/GP gives exact rank 5 and torsion C2 x C4.",
  "created_at": "2026-09-28 17:44:24",
  "updated_at": "2026-09-28 17:44:24"
}