{
  "id": 5239,
  "curve_key": "49700928816:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1035436017",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 73.88786837497521,
  "faltings_height": 4.225562776222758,
  "conductor": "34308087849626377248",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "41",
    "59",
    "109"
  ],
  "discriminant": "71047659667806461991617082432",
  "regulator": "19054.433278892900193867014117513522233995217253944",
  "points": [
    [
      "-29028",
      "2365782"
    ],
    [
      "-9471",
      "2992836"
    ],
    [
      "-7257",
      "2670576"
    ],
    [
      "-2943",
      "1738332"
    ],
    [
      "72688",
      "17572324"
    ],
    [
      "-9471/4",
      "12492249/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (1,6,17,21), 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 10:52:56",
  "updated_at": "2026-10-21 10:52:56"
}