{
  "id": 5210,
  "curve_key": "1016496:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-21177",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 41.49561593091442,
  "faltings_height": 1.5262084058843586,
  "conductor": "1594543392",
  "bad_primes": [
    "2",
    "3",
    "13",
    "181"
  ],
  "discriminant": "607817617422912",
  "regulator": "55.22018662897916614699147957419890793848916546",
  "points": [
    [
      "-117",
      "936"
    ],
    [
      "-36",
      "846"
    ],
    [
      "147",
      "252"
    ],
    [
      "156",
      "702"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (1,6,10,15), 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. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.",
  "created_at": "2026-10-21 10:13:46",
  "updated_at": "2026-10-21 10:13:46"
}