{
  "id": 5248,
  "curve_key": "1083563140435776:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-22574232092412",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 103.8570936291628,
  "faltings_height": 6.722998214071724,
  "conductor": "113243545458240858601772832",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "37",
    "43",
    "53"
  ],
  "discriminant": "736239190504878137330660086839951825825792",
  "regulator": "36476823.6361314342850534859583554851605885230330093915",
  "points": [
    [
      "-3949491",
      "5248873539"
    ],
    [
      "-2541678",
      "6399755172"
    ],
    [
      "5764122",
      "7835363172"
    ],
    [
      "108237402",
      "1124986252572"
    ],
    [
      "-115347414/121",
      "6048859101012/1331"
    ],
    [
      "-16285983/16",
      "299661754833/64"
    ],
    [
      "-74175/16",
      "20704037535/64"
    ],
    [
      "506751232/81",
      "7421415646112/729"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5247: https://elliptic-rank.icarm.cloud/curve/5247. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (2,14,18,22), 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. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C2.",
  "created_at": "2026-10-21 11:04:51",
  "updated_at": "2026-10-21 11:04:51"
}