{
  "id": 5340,
  "curve_key": "86674082602800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1805710054225",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 96.27952806932711,
  "faltings_height": 6.09153441741875,
  "conductor": "4173553663909443123648800",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "19",
    "43",
    "71",
    "103",
    "157"
  ],
  "discriminant": "376811390638443398414671401392809000000",
  "regulator": "8466389.86349154947680337314493944990954855804791931246",
  "points": [
    [
      "-656260",
      "949936350"
    ],
    [
      "-244240",
      "653036700"
    ],
    [
      "8277500",
      "23498994750"
    ],
    [
      "455834225",
      "9732143582700"
    ],
    [
      "-2300267585/31329",
      "2016092527549100/5545233"
    ],
    [
      "-21457975/16",
      "6244270725/64"
    ],
    [
      "-9055760/9",
      "24122280700/27"
    ],
    [
      "345590441/121",
      "5669065594164/1331"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny endpoint from the Aguirre–Castañeda–Peral parametrization at tuple (13,18,23,27), 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.",
  "created_at": "2026-10-21 14:11:15",
  "updated_at": "2026-10-21 14:11:15"
}