Elliptic curves with high rank

Bachelor thesis (2014)

Authors

Contributors

R.M. Van Luijk (mentor)
K.P. Hart (mentor)
Programme
Industrial and Applied Mathematics (EEMCS) (TU Delft)
Copyright: © 2014 Bik, M.A.
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Published Date

03-10-2014

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Programme

Industrial and Applied Mathematics

Abstract

In this thesis we will look at methods for constructing elliptic curves over Q with high ranks. Using these methods we find an elliptic curve with rank at least 13, an infinite family of elliptic curves with rank at least 9, an elliptic curve with rank at least 10 and torsion-subgroup Z/2Z and an infinite family of elliptic curves with rank at least 8 and with torsion point of order 2.