昨天无意中发现原来我有一个5分币不一样，上网一搜，原来是非流通的版本。呵呵，最近quarter已经达到38枚了，继续

顺便在littletoncion order了20枚5分币

2004 Peace Medal Nickel

2005 Keelboat Nickel

2005 Bison Nickel

2005 Ocean in View Nickel

2006 New Jefferson Portrait

每种4枚，一个gold-plated 一个colorized 两个普通的 一共9.95已经不到3折了

原价要>34,还送一个2003Jefferson Nickel

 

 

 

 2005 designs

On September 16, 2004, the U.S. Mint unveiled its new designs for 2005. They had been chosen by John W. Snow on July 22, 2004 but were not disclosed to the public. The U.S. Mint revealed that the Felix Schlag depiction of Thomas Jefferson was being done away with in favor of a more modern depiction of Jefferson. The new obverse of the Jefferson nickel was designed by Joe Fitzgerald and engraved by Don Everhart II. Its circulation began on February 28, 2005.

Also unveiled on September 16, 2004 were two new reverses. A depiction of the American bison temporarily returns to the reverse after a 67-year absence. The new reverse was designed by Jamie N. Franki and engraved by Norman E. Nemeth. The U.S. Mint had been lobbied to include the American bison on the nickel in the hope of keeping the public interested in its continuing recovery after nearly being hunted to extinction after the completion of the transcontinental railroad.

when we consider elliptic curve with complex multiplication by $O$,  by class field theory, there exists an abelian extension $H_c$ of $K$, which is unramified outside of the primes dividing $c$, where $c$ is the conductor, and whose Galois group is naturally identified, via the Artin map, with Picard group of $O$.

 

For the algebraic property of $j(O)$, it suffices to show it has only finite conjugate under the action of $Gal(C/Q)$, since we have related $O$ to an elliptic curve and only finitely many classes of EC have CM by $O$, it's safe to conclude that

 $j(O)$ is algebraic.

 

In fact, Heegner point on modular curve of level $N$ is also defined in this way, a pair of ECs have the same complex multiplication and joined by an $N$-isogeny.

 

D. Hilbert once said that: The theory of complex multiplication is not only the most beautiful part of mathematics but also of all science.

You'd better believe him, it's true,lol.