{
  "id": 5231,
  "curve_key": "-2667381024:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "55570438",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 65.11308881425087,
  "faltings_height": 3.4943311461623967,
  "conductor": "197636709088758016",
  "bad_primes": [
    "2",
    "7",
    "11",
    "23",
    "29",
    "541"
  ],
  "discriminant": "-10982758488940863825131008",
  "regulator": "18592.481892992990042720634717752266491642078661123",
  "points": [
    [
      "1082",
      "247778"
    ],
    [
      "3887",
      "524147"
    ],
    [
      "14168",
      "1905596"
    ],
    [
      "27050",
      "4614730"
    ],
    [
      "41657/4",
      "10455907/8"
    ],
    [
      "41657/16",
      "25785683/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (6,11,21,22), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 10:41:51",
  "updated_at": "2026-10-21 10:41:51"
}