From the Super Mario Wiki
Egg 1 is Yoshi's original kart in Mario Kart DS. It is essentially a Yoshi Egg on wheels. The Egg 1 has above average speed, high acceleration, and high handling, but also has low drift, weight, and items. Its name is clearly a pun on F-1 (Formula One).
The Egg 1 reappears as a retro kart body in Mario Kart 7. It is one of the unlockable kart bodies in the game.
Mario Kart DS
Mario Kart 7
Names in other languages