{
  "id": 5214,
  "curve_key": "-9416064:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "196168",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 48.17378317452158,
  "faltings_height": 2.082722342851622,
  "conductor": "153927536896",
  "bad_primes": [
    "2",
    "7",
    "31",
    "113"
  ],
  "discriminant": "-483130512925032448",
  "regulator": "1060.21870977981355080077857421589342783340692928",
  "points": [
    [
      "32",
      "2512"
    ],
    [
      "113",
      "4859"
    ],
    [
      "128",
      "5216"
    ],
    [
      "2825",
      "151985"
    ],
    [
      "113/4",
      "18871/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5213: https://elliptic-rank.icarm.cloud/curve/5213. Obtained from the Aguirre–Castaneda–Peral parametrization 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 10:20:34",
  "updated_at": "2026-10-21 10:20:34"
}