{
  "id": 5305,
  "curve_key": "1888077936:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-39334957",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 64.07647555043627,
  "faltings_height": 3.4079467075111793,
  "conductor": "49511642950139168",
  "bad_primes": [
    "2",
    "17",
    "53",
    "149",
    "293"
  ],
  "discriminant": "3895076692886154634591552",
  "regulator": "21165.341449033988405894256017221665341797508008557",
  "points": [
    [
      "-4981",
      "268974"
    ],
    [
      "-3604",
      "308142"
    ],
    [
      "-2533",
      "288762"
    ],
    [
      "-293",
      "107238"
    ],
    [
      "-212",
      "91266"
    ],
    [
      "-54272/9",
      "3614176/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5304: https://elliptic-rank.icarm.cloud/curve/5304. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,8,11,20), 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 12:48:44",
  "updated_at": "2026-10-21 12:48:44"
}