An algorithm for determining torsion growth of elliptic curves
Abstract:
We present a fast algorithm that takes as input an elliptic curve defined over \(\mathbb Q\) and an integer \(d\) and returns all the number fields \(K\) of degree \(d'\) dividing \(d\) such that \(E(K)_{tors} \supsetneq E(F)_{tors}\), for all \( F\subsetneq K\). We ran this algorithm on all elliptic curves of conductor less than 400.000 (a total of 2.483.649 curves) and all \(d \leq 23\).
Magma script related to prove some results at section 2 and 5 README
Auxiliary files from other articles:
- 2primary_Ss.txt from this webpage
E. González-Jiménez, and Á. Lozano-Robledo. On the minimal degree of definition of p-primary torsion subgroups of elliptic curves. Math. Res. Lett. 24 (2017) 1067-1096.
Download the PDF and then click in the
text
to open a file with magma source proving the corresponding result.
Here you can download all the necessary files zipped
Last modified: 14/4/2019