{
  "id": 3343,
  "curve_key": "22082001328:-3258727923692800",
  "ainvs": [
    "0",
    "1",
    "0",
    "-460041694",
    "3771522490376"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 71.4540860823085,
  "faltings_height": 3.8038228874717324,
  "conductor": "100389817248",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "37",
    "41",
    "71",
    "73"
  ],
  "discriminant": "85765391996521936805112384",
  "regulator": "10290.0517528930204737439952204345349568337284135",
  "points": [
    [
      "226553/16",
      "-19894635/64"
    ],
    [
      "15014",
      "-499140"
    ],
    [
      "2999702/169",
      "-2405006700/2197"
    ],
    [
      "35558",
      "5689740"
    ],
    [
      "367286/25",
      "-53624916/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1642 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-26 21:05:19",
  "updated_at": "2026-09-26 21:05:19"
}