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Something that may help:
k.<a,b>=NumberField([x^2 - 30*x + 2817,x^4 + 30*x^3 - 18252*x^2 + 280530*x +6465339])
kX.<X>=FunctionField(k)
R.<Y> = kX[]
kY.<Y> = kX.extension(Y^2-X^3+3267*X-45630)
E=EllipticCurve(kY,[-3267,45630])
Q=E([X,Y])
P1=E([15,0])
P2=E([1/5184*(-b^3 - 45*b^2 + 14985*b - 133515),0])
print(P1+Q)
print(P2+Q)
Here the answer is as follows:
((15*X - 2817)/(X - 15) : ((-2592)/(-X^2 + 30*X - 225))*Y : 1)
and
(((-1/5184*b^3 - 5/576*b^2 + 185/64*b - 4945/192)*X + 5/864*b^3 +
25/96*b^2 - 2775/32*b + 114869/32)/(X + 1/5184*b^3 + 5/576*b^2 -
185/64*b + 4945/192) : ((5/576*b^3 + 25/64*b^2 - 8325/64*b +
449151/64)/(-X^2 + (-1/2592*b^3 - 5/288*b^2 + 185/32*b - 4945/96)*X -
5/1728*b^3 - 25/192*b^2 + 2775/64*b - 219413/64))*Y : 1).
