pdf

data

Growth of torsion groups of elliptic curves upon base change

Enrique González-Jiménez and Filip Najman

---

Data (Magma):

Magma script related to prove the following result:

• Section 5:
  

  Proposition 5.4	Lemma 5.5	Theorem 5.6	Theorem 5.8

  
  
• Section 6: Given a positive integer d the function RQ(d) computes the set of primes p for which there exists a number field K of degree exactly d and an elliptic curve E defined over the rationals, such that p divides the order of the torsion subgroup of E(K): RQ.txt
  
  
• Section 7:
  

  Proposition 7.1 (a)	Proposition 7.1 (b)	Proposition 7.7

  
  
• Section 8:
  

  Proposition 8.1	Lemma 8.11	Lemma 8.14	Lemma 8.15 (a)	Lemma 8.15 (b)

  
  
• Appendix:
  

  Table 1 and 2

• Translation between labels in Zywina and Sutherland notation: Zywina-Sutherland_labels.txt

Auxiliary files from other articles:

• subgroups.m from Sutherland's webpage
  A.V. Sutherland. Computing images of Galois representations attached to elliptic curves. Forum Math. Sigma 4 (2016), e4.
  
• Equations.txt from Zywina's webpage
  D. Zywina. On the possible images of the mod l representations associated to elliptic curves over Q. arXiv:1508.07660.
  
• 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.

---