{
  "id": 5270,
  "curve_key": "127296576:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2652012",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 55.986090498217266,
  "faltings_height": 2.733747953159596,
  "conductor": "1562926144032",
  "bad_primes": [
    "2",
    "3",
    "11",
    "37",
    "181"
  ],
  "discriminant": "1193730880056938606592",
  "regulator": "1111.51742137141761662033809635254175775700376118",
  "points": [
    [
      "-1628",
      "1628"
    ],
    [
      "-1584",
      "15048"
    ],
    [
      "1764",
      "28476"
    ],
    [
      "5328",
      "370296"
    ],
    [
      "-3663/4",
      "326007/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5269: https://elliptic-rank.icarm.cloud/curve/5269. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,4,9,16), 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 11:40:07",
  "updated_at": "2026-10-21 11:40:07"
}