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= Suggested Problems =
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Suggested Problems

Suggested Problems

1. Consider the rational function field Q(d) in one variable d.  

a. Create in Sage the elliptic curve with a-invariants 

   (a1, a2, a3, a4, a6) = (1+d-d^2, d^2-d^3, d^2-d^3, 0, 0)

that appears on page 2 of Elkies' slides.   

b. Put it in short Weierstrass form y^2 = x^3 + A*x + B.

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2.

a. Find a quadratic imaginary number field with class number 5.

b. Find a cubic field with class number 3. 

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3.

For a given integer a, let 
 
   E = EllipticCurve([0,(a-1),1,-a,0])

For r = 0, 1, 2, 3, 4, 5, find the smallest positive integer a such
that E has rank r.

jmm12/probs (last edited 2012-01-02 20:00:44 by was)