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alexjbest/L-ec-ff.sage

Created October 17, 2019 02:08
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  1. alexjbest created this gist Oct 17, 2019.
    18 changes: 18 additions & 0 deletions L-ec-ff.sage
    View file
    Original file line number Diff line number Diff line change
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    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