{
  "id": 5272,
  "curve_key": "-4225544064:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "88032168",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 66.49324158602836,
  "faltings_height": 3.609343877143854,
  "conductor": "3444294490124544",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "29",
    "317"
  ],
  "discriminant": "-43662054412241020559720448",
  "regulator": "6963.5217077078636442703882662254855369380350009688",
  "points": [
    [
      "609",
      "232029"
    ],
    [
      "928",
      "287216"
    ],
    [
      "2536",
      "489448"
    ],
    [
      "6657",
      "938637"
    ],
    [
      "9576",
      "1311912"
    ],
    [
      "38304",
      "7718256"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5271: https://elliptic-rank.icarm.cloud/curve/5271. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,8,10,12), 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 11:42:58",
  "updated_at": "2026-10-21 11:42:58"
}