some sage code to compute L-functions of elliptic curves over function field of genus 0

L-ec-ff.sage

p=7
L.<t> = FunctionField(GF(p))
S.<x,y> = L[] 
E = EllipticCurve(y^2 - x*(x-1)*(x-t^2))
deg = 3 # what degree correct up till
R.<T>= PowerSeriesRing(QQ)
lpol = ((1 + T) * (1 - T))^(-2) # bad factors computed by hand for now
ll = []
for N in range(deg + 1): 
    for pp in L.places(N):
        try:  
            Epp = E.base_extend(lambda x: x.evaluate(pp)) 
        except:
            print "bad", pp 
            pass  
        else: 
            lpol *= (1 - ((p^N  + 1) - Epp.cardinality()) * T^N + p^N * T^(2*N))^(-1)
print lpol