{
  "id": 5241,
  "curve_key": "-998158037184:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "20794959108",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 82.88753236383901,
  "faltings_height": 4.975534775294742,
  "conductor": "96095627622976034592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "67",
    "71",
    "83"
  ],
  "discriminant": "-575511738300685981614134437613568",
  "regulator": "34991.86022742262041584364940380427888439445127371234",
  "points": [
    [
      "14058",
      "17178876"
    ],
    [
      "38346",
      "29219652"
    ],
    [
      "121429",
      "65693089"
    ],
    [
      "126522",
      "68237532"
    ],
    [
      "194469",
      "106763481"
    ],
    [
      "227088",
      "128191176"
    ],
    [
      "777876",
      "697754772"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5240: https://elliptic-rank.icarm.cloud/curve/5240. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,15,16,18), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 10:55:15",
  "updated_at": "2026-10-21 10:55:15"
}