{
  "id": 5333,
  "curve_key": "-765019975104:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "15937916148",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 82.08950334503734,
  "faltings_height": 4.909032357061268,
  "conductor": "56448260253484257312",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "59",
    "223"
  ],
  "discriminant": "-259104279922707835548493019762688",
  "regulator": "771047.8864977837996198933402942975933722314083810113",
  "points": [
    [
      "253",
      "2008061"
    ],
    [
      "669",
      "3265389"
    ],
    [
      "966",
      "3923892"
    ],
    [
      "2622",
      "6465852"
    ],
    [
      "3594486",
      "6819034572"
    ],
    [
      "7659381",
      "21200665527"
    ],
    [
      "93214/25",
      "964019188/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5332: https://elliptic-rank.icarm.cloud/curve/5332. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,8,23,25), 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 13:32:10",
  "updated_at": "2026-10-21 13:32:10"
}