{
  "id": 5212,
  "curve_key": "-28991424:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "603988",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 51.547531860233434,
  "faltings_height": 2.3638680666609435,
  "conductor": "729603008288",
  "bad_primes": [
    "2",
    "7",
    "11",
    "37",
    "53"
  ],
  "discriminant": "-14101486776635281408",
  "regulator": "918.986275113607151189857400843051402028612102148",
  "points": [
    [
      "53",
      "5671"
    ],
    [
      "77",
      "6853"
    ],
    [
      "848",
      "33496"
    ],
    [
      "1232",
      "51128"
    ],
    [
      "1325",
      "55915"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5211: https://elliptic-rank.icarm.cloud/curve/5211. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (8,12,15,16), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 10:17:54",
  "updated_at": "2026-10-21 10:17:54"
}