{
  "id": 5218,
  "curve_key": "-29436624:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "613263",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 51.59325051400905,
  "faltings_height": 2.367677954475578,
  "conductor": "12034928229408",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "29",
    "53"
  ],
  "discriminant": "-14761152381502876608",
  "regulator": "820.732876610346838150920922371160712295826185983",
  "points": [
    [
      "57",
      "5928"
    ],
    [
      "399",
      "17556"
    ],
    [
      "513",
      "21204"
    ],
    [
      "1596",
      "71022"
    ],
    [
      "3591",
      "220248"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (1,2,9,22), 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. Selected in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 10:24:55",
  "updated_at": "2026-10-21 10:24:55"
}