### 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 $$d \leq 23$$.

### Computational Results

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.