{
  "id": 5220,
  "curve_key": "32898096:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-685377",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 51.926776025161516,
  "faltings_height": 2.395471747071617,
  "conductor": "1670192469792",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "43"
  ],
  "discriminant": "20604807078635368512",
  "regulator": "206.181580004671433934602212509968483476323436940",
  "points": [
    [
      "-759",
      "9108"
    ],
    [
      "-33",
      "4752"
    ],
    [
      "924",
      "12474"
    ],
    [
      "5313",
      "382536"
    ],
    [
      "5313/4",
      "302841/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (3,5,9,10), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 10:27:32",
  "updated_at": "2026-10-21 10:27:32"
}