{
  "id": 5335,
  "curve_key": "-69901410440450635200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1456279384176054900",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 137.08085250271196,
  "faltings_height": 9.491644786867488,
  "conductor": "18851107953566130654892075802791200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "47",
    "79",
    "109",
    "131",
    "907"
  ],
  "discriminant": "-197657855147920430008973077289309038556690095945536000000",
  "regulator": "1112092583.7142824130558452662985650690532745252162500700",
  "points": [
    [
      "17373510",
      "5030499820500"
    ],
    [
      "1121875524",
      "55188422652132"
    ],
    [
      "2616588990",
      "147394234633500"
    ],
    [
      "3000152269",
      "177124733931797"
    ],
    [
      "44607465/4",
      "32240714440725/8"
    ],
    [
      "5868385600/9",
      "945685938150800/27"
    ],
    [
      "230695093750/81",
      "120340582294872500/729"
    ],
    [
      "271124654350/2209",
      "1395202591041321700/103823"
    ],
    [
      "2611165282110/1681",
      "5343089498045352900/68921"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5334: https://elliptic-rank.icarm.cloud/curve/5334. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,5,16,25), 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 13:39:41",
  "updated_at": "2026-10-21 13:39:41"
}