{
  "id": 5213,
  "curve_key": "2354016:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-49042",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 44.01490009116191,
  "faltings_height": 1.7361487525716495,
  "conductor": "153927536896",
  "bad_primes": [
    "2",
    "7",
    "31",
    "113"
  ],
  "discriminant": "7548914264453632",
  "regulator": "530.109354889906775400389287107946713916703464642",
  "points": [
    [
      "-217",
      "651"
    ],
    [
      "-62",
      "1674"
    ],
    [
      "224",
      "504"
    ],
    [
      "343",
      "4851"
    ],
    [
      "-1736/9",
      "40796/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (1,2,10,11), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 10:19:20",
  "updated_at": "2026-10-21 10:19:20"
}