{
  "id": 5208,
  "curve_key": "-643104:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "13398",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 40.12218519592831,
  "faltings_height": 1.4117558446355163,
  "conductor": "11488409856",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "29"
  ],
  "discriminant": "-153921715250688",
  "regulator": "103.0761310278705121743825142108443322498445761",
  "points": [
    [
      "42",
      "798"
    ],
    [
      "58",
      "986"
    ],
    [
      "88",
      "1364"
    ],
    [
      "378",
      "7686"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (5,14,18,21), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Selected in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.",
  "created_at": "2026-10-21 10:09:39",
  "updated_at": "2026-10-21 10:09:39"
}