{
  "id": 5209,
  "curve_key": "702576:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-14637",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 40.38752657817551,
  "faltings_height": 1.4338676264894499,
  "conductor": "6855736608",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "41"
  ],
  "discriminant": "200694833462592",
  "regulator": "65.04883192446198650465198160757752600804799882",
  "points": [
    [
      "-119",
      "238"
    ],
    [
      "-84",
      "798"
    ],
    [
      "-21",
      "546"
    ],
    [
      "-119/4",
      "5117/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (4,6,15,16), 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 10:12:24",
  "updated_at": "2026-10-21 10:12:24"
}