{
  "id": 5233,
  "curve_key": "19109156976:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-398107437",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 71.02030043981945,
  "faltings_height": 3.9865987816264443,
  "conductor": "5071665004630687008",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "23",
    "47",
    "71"
  ],
  "discriminant": "4038135112632231872608156992",
  "regulator": "13187.890026600013655006887129445329183219379843058",
  "points": [
    [
      "-19383",
      "659022"
    ],
    [
      "-4277",
      "1274546"
    ],
    [
      "-2679",
      "1023378"
    ],
    [
      "46683",
      "9118746"
    ],
    [
      "295113",
      "159951246"
    ],
    [
      "-76751/64",
      "353131351/512"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,12,16,17), 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 10:44:43",
  "updated_at": "2026-10-21 10:44:43"
}