{
  "id": 5242,
  "curve_key": "268393633200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5591534025",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 78.94716156135333,
  "faltings_height": 4.647170541754267,
  "conductor": "330739863830560800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "43",
    "89"
  ],
  "discriminant": "11188526372296307665588881000000",
  "regulator": "42428.237200369877293585104188197041894054902082278",
  "points": [
    [
      "-1155",
      "2541000"
    ],
    [
      "-644",
      "1897546"
    ],
    [
      "307395",
      "165310200"
    ],
    [
      "641355",
      "510123900"
    ],
    [
      "4784395",
      "10463753300"
    ],
    [
      "-18975/4",
      "41118825/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,6,12,20), 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. Selected in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 10:56:22",
  "updated_at": "2026-10-21 10:56:22"
}