{
  "id": 5221,
  "curve_key": "-131592384:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "2741508",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 56.08565910852119,
  "faltings_height": 2.74204533735159,
  "conductor": "1670192469792",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "43"
  ],
  "discriminant": "-1318707653032663584768",
  "regulator": "412.363160009342867869204425019936966952646873879",
  "points": [
    [
      "154",
      "20636"
    ],
    [
      "322",
      "30268"
    ],
    [
      "1012",
      "61732"
    ],
    [
      "1978",
      "114724"
    ],
    [
      "2898",
      "179676"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5220: https://elliptic-rank.icarm.cloud/curve/5220. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,5,9,10), 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 10:28:45",
  "updated_at": "2026-10-21 10:28:45"
}