{
  "id": 5223,
  "curve_key": "150209136:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3129357",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 56.48261736303126,
  "faltings_height": 2.775125191894096,
  "conductor": "313372007470368",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "31"
  ],
  "discriminant": "1961305770362896786752",
  "regulator": "1472.4639559029447247399718710320440573655950741719",
  "points": [
    [
      "-1767",
      "3534"
    ],
    [
      "-1463",
      "38038"
    ],
    [
      "-341",
      "32054"
    ],
    [
      "4123",
      "239134"
    ],
    [
      "7161",
      "587202"
    ],
    [
      "-4991/9",
      "1068074/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,12,18,21), 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 10:30:07",
  "updated_at": "2026-10-21 10:30:07"
}