{
  "id": 5311,
  "curve_key": "387905856:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-8081372",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 59.32881968691193,
  "faltings_height": 3.012308718884151,
  "conductor": "130617146804768",
  "bad_primes": [
    "2",
    "13",
    "23",
    "29",
    "233"
  ],
  "discriminant": "33778104093054130614272",
  "regulator": "7065.3336253517796691711269526374116711846161054094",
  "points": [
    [
      "-2691",
      "47541"
    ],
    [
      "-2668",
      "50692"
    ],
    [
      "-667",
      "71369"
    ],
    [
      "4212",
      "201708"
    ],
    [
      "6032",
      "413192"
    ],
    [
      "-8671/4",
      "685009/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5310: https://elliptic-rank.icarm.cloud/curve/5310. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (8,16,19,22), 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.",
  "created_at": "2026-10-21 13:01:06",
  "updated_at": "2026-10-21 13:01:06"
}