# Multiplication polynomials and relative Manin-Mumford

Schmidt, Harry. Multiplication polynomials and relative Manin-Mumford. 2015, Doctoral Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_11526

After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is $(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the discriminant of the  curve. In the appendix we give an application to good reduction of an associated Latt\`es map. We also prove a similar result for the discriminant of the largest square free factor of $B_n$.