{
  "id": 3564,
  "curve_key": "-83808192:226065931776",
  "ainvs": [
    "0",
    "0",
    "0",
    "1746004",
    "-261650384"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4
  ],
  "naive_height": 54.732123951713085,
  "faltings_height": 2.6357637569985246,
  "conductor": "84722624",
  "bad_primes": [
    "2",
    "7",
    "281",
    "673"
  ],
  "discriminant": "-370230832098905817088",
  "regulator": "2213.320351555982757783090095417722454016879509",
  "points": [
    [
      "4393/16",
      "988245/64"
    ],
    [
      "1669",
      "85449"
    ],
    [
      "3748",
      "242760"
    ],
    [
      "1321/4",
      "149877/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "2-isogenous quotient of curve#3392 by the rational 2-torsion point (-74,0). Torsion Z/4Z; PARI/GP ellrank gives [4,4,0], so the rank is exactly 4. The four witnesses are the images of the independent witnesses of curve#3392 under the degree-2 isogeny. Naive height 54.7321239517, improving the previous Z/4Z rank>=4 naive-height record 55.3300822300 in the 2026-09-27 catalogue.",
  "created_at": "2026-09-28 15:24:55",
  "updated_at": "2026-09-28 15:24:55"
}