{
  "id": 5251,
  "curve_key": "-19152:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "399",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 29.580487283393264,
  "faltings_height": 0.533281018590929,
  "conductor": "5094432",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19"
  ],
  "discriminant": "-4065356736",
  "regulator": "11.687107420268947303287579261049035695189752",
  "points": [
    [
      "1",
      "20"
    ],
    [
      "7",
      "56"
    ],
    [
      "25",
      "160"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (1,3,12,14), 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 11:13:19",
  "updated_at": "2026-10-21 11:13:19"
}