I didn't recall the model name but it has to be an Electrum  ser#86E4159. I'm the original owner. Purchase at Zapf's in Philly in 86-87.
 

That's actually one of the California Specials. Very gorgeous guitar! Don't see these very often
 
~Taylor

Really?... cool! I'm waiting to hear what Mica has to say on it. I've not seen another like it.

It's one of the guitars I dream about, a California Special.  
 
Does it make a California Special Dreaming?

It's interesting as it doesn't have the CS in the serial#... I'd love to know what she's valued at these days.

well let me rephrase that, it has all the makings of California Special, same body and headstock shape, Kahler tremolo, but the electronics are that of an Electrum with 3 pickups, the only difference being the Electrums have the 5-way pickup selector, as seen here http://club.alembicguitars.net/Images/411/15011.html?1155134366, and the California Specials have 3 on/off switches instead, seen here http://club.alembicguitars.net/Images/411/56053.html?1224687699. So it could be designated as an Electrum based off the electronics in it.  
 
~Taylor

The body seems to me to be a little different than a California Special.  The horns are a little longer and curve in a bit more than on the Cali.  Also, the lower bout seems a little narrower.  Electrums came in both two and three pick-up configurations.  My guess is that this is a custom bodied Electrum.  I'm sure Mica will soon chime in with the definitive answer.  Cool guitar - enjoy!
 
Bill, the guitar one

Thanks Bill,
 
I've not seen another one like this anywhere. With the E in the serial# I think you're onto something.  
 
Many years ago, I called Alembic to get an idea of value for an insurance rider. I believe it was Mica who I spoke with. I told her the serial number and she paused and then said Ohhh, you have that one!

If it were a bass, the body shape would be called a Vector. California Specials would appear to have skinnier horns. Nice one, whichever way you want to name it.