Sage has the ability to compute the Heegner points over ring class fields.
I would like to compute the trace of the Heegner point defined over the
Hilbert class field down to K. Apparently this is not implemented in sage,
but coding it should be easy. However I'm having an issue with the code
below
E=EllipticCurve('75a1')
P=E.heegner_point(-56)
# Note that K=Q(sqrt(-56)) has class number 4
P_conj=P.conjugates_over_K() #These are the 4 conjugates of the Heegner
point P
P_trace=P_conj[0].point_exact()+P_conj[1].point_exact()+P_conj[2].point_exact()+P_conj[3].point_exact()
P_trace should be the desired trace of P down to K. When one prints P_trace
we see that it is a point in projective space whose 3rd coordinate is 1 so
the 1st and second coordinates should be in K. However if we try
P_trace[0].minpoly('x'), we get a polynomial of degree 4. What am I doing
wrong?
Ahmed
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