{
  "id": 3341,
  "curve_key": "-535507919:-78002274754729",
  "ainvs": [
    "1",
    "0",
    "0",
    "11156415",
    "90281340297"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6
  ],
  "naive_height": 63.97551821143012,
  "faltings_height": 3.3923675573846857,
  "conductor": "45225870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "41",
    "83",
    "443"
  ],
  "discriminant": "-3609908445284280868032000",
  "regulator": "131.14777551291934873929853554304780385909927",
  "points": [
    [
      "28194",
      "4762563"
    ],
    [
      "17502",
      "2367555"
    ],
    [
      "-2478",
      "219003"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1799 (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 3 carries over. Torsion ℤ/6ℤ.",
  "created_at": "2026-09-26 21:03:40",
  "updated_at": "2026-09-26 21:03:40"
}