Toyota is one of the biggest automakers in the world. But unlike its rivals at GM with their Corvettes and Volkswagen with their Lamborghinis and Bugattis, the Japanese giant doesn’t have much of a history making supercars.

This was the exception. It’s a Lexus LFA, which is hardly what you’d call “common,” with only 500 examples made. But this one is equipped with the Nürburgring package, making it even more rare and desirable, and it’s coming up for auction.

The LFA was one of the most exotic supercars ever made in Japan, and the lucky beneficiary of Toyota’s considerable resources. As the story goes, it was originally engineered out of aluminum, but sent back to the drawing board to be completely redesigned out of carbon fiber – at untold cost but to spectacular effect.

In its nose sat a 4.8-liter V10, screaming in naturally aspirated form all the way to its stratospheric 9,000-rpm redline. It was capable of producing 560 metric horsepower and 354 lb-ft (480 Nm) of torque – which was a little behind the times at the start of this decade, but it was highly rated for its driving dynamics. In fact Car and Driver favored it over the contemporary Ferrari 599 GTB (even with the optional HGTE package) when it pitted the two against each other late in 2010.

The Nürburgring Package took things even further. It added an extra 10 horsepower, a recalibrated transmission, a more extreme aero kit, and a stiffer suspension with lighter wheels and stickier tires. Only 50 of these were made, cementing this special LFA’s place as the fastest, most exotic supercar Toyota ever made – that is, this side of the GT-One homologation special, of which only two road-going examples were produced.

This example has had just one owner, who has put just 1,600 miles (2,574 km) on it. Barrett-Jackson will auction it off at its sale in Florida next month, so if you want to get your hands on this rare specimen, West Palm Beach will be the place to be.