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Explicit representation of element of ideal

P.<x,y,z,t>=PolynomialRing(QQ,4) 
C1= 17*x^2 + 7*y^2 - 26*y*z + 7*z^2
C2= 13*y^2 - 7*y*z + 13*z^2 - 51*t^2
x^4+y^4+z^4-18*t^4 in ideal(C1,C2)

So there exist \alpha, \beta in P with <latex>\alpha C1 + \beta C2 = x^4+y^4+z^4-18*t^4</latex>

What's the command to find \alpha and \beta explicitly ?