I got an '01 Skorpion in October, and the battery failed pretty quickly. I ran it a while on the battery from my '95, then sold that bike.
I finally installed a replacement in the '01, with simple modification to the battery tray. My new 14 Amp-Hour AGM (absorbed glass matt) battery is built by Johnson Controls in Taiwan, sold by WalMart in the US as their EverStart number ES14-BS. $65.00 plus $9 core charge and sales tax. In inches, they list it as 6" long x 3.44" wide x 4.19" high, the same as their $55 AH model ES9-BS.
This 6" long battery is longer than the tray section of the airbox by about 1/8" (3mm). I used a heat gun on the 800 deg F setting, and warmed the plastic airbox sides near the roots of the corners, then used the round end of a large box-end wrench to push and form the softened plastic, mostly moving out the bottom and side corners a little bit. It did not take much reshaping to make the battery fit easily. Go easy on the heat, a hair dryer would not be enough, but you could easily destroy/crack/puncture the airbox if you are not careful with a true heat gun.
I did not replace my ground wires with longer leads, but that would be preferable. In order to place the ground terminal on the left side of the bike, the battery is turned with the terminals forward, under the frame strap (where the seat hooks). I needed to attach and tighten the connections while the battery was partially inserted into the tray. There is a short circuit hazard during installation, and with battery movement and uninsulated positive terminal. With longer ground leads, the terminals could be rearward, and not near that metal frame. I do intend to use longer leads, and reverse the battery. Today, I do have the insulating hood on the positive terminal, and worked out a retention strap to keep the battery from moving.
The original 'hook' for the o-ring battery retention on the bottom of the tray will not work with this wider (deeper) battery. I intend to build a alternate hook, and get a longer o-ring. Today, I grabbed a few zip-ties and put about 4 in series to make a long loop around the neck at the top of the shock body (at the eye, where its movement is minimal). The top of the loop is hooked around the original o-ring peg on the frame strap, and did not need to be cinched down hard to appropriately retain the battery.
I'm guessing the cranking speed is improved 20% over the smaller batteries in either of these bikes. Other than these two, I've never even seen another 660 Yamaha, and don't know if these have been typical.
Cheers,
Mark
San Carlos, California
P.S.
I wish the EverStart line had a 7AH AGM battery, I would have chosen that for the upgrade I just did on my KTM 400 EXC dirtbike. The Yuasa I bought had list price at $110! I am aware that the BikeMaster brand has a reasonably priced 7AH AGM, but it wasn't available when/where I needed it.