{
  "id": 3474,
  "curve_key": "15081991471775761:291957023191448192470759",
  "ainvs": [
    "1",
    "1",
    "1",
    "-314208155661995",
    "-337913352206463230080"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 111.7568334277016,
  "faltings_height": 7.379782996798567,
  "conductor": "10196321216235",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "59",
    "149",
    "3109"
  ],
  "discriminant": "1936000236295596876521355341643846645875390625",
  "regulator": "2183.80024789901072662966740852258475523428790334",
  "points": [
    [
      "-4026630",
      "29361847870"
    ],
    [
      "-2681607",
      "22032817543"
    ],
    [
      "19153598",
      "25885701263"
    ],
    [
      "92389767/4",
      "549931834979/8"
    ],
    [
      "-25719307/16",
      "817171591957/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found by a conductor-oriented search in the standard Z/2Z x Z/4Z family \\(y^2=x(x+u^2)(x+v^2)\\), using conditions \\(u+v=d w^2\\) with small squarefree \\(d\\). Here \\((u,v)=(8791,11900)\\) and \\(u+v=20691=19\\cdot33^2\\). PARI/GP 2.17.4 gives exact rank 5 and torsion Z/2Z x Z/4Z. Conductor \\(N=10196321216235\\). This improves my preceding rank-5 submission of conductor \\(38019384450552\\).",
  "created_at": "2026-09-27 08:01:24",
  "updated_at": "2026-09-27 08:01:24"
}