Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2013
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1303.3500 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- Let A=E_1xE_2 be be the product of two elliptic curves over QQ, both having a rational five torsion point P_i. Set B=A/<(P_1,P_2)>. In this paper we give an algorithm to decide whether the Tate-Shafarevich group of the abelian surface B has square order or order five times a square, assuming that we can find a basis for the Mordell-Weil groups of both E_i, and that the Tate-Shafarevich groups of the E_i are finite. We considered all pairs (E_1,E_2), with prescribed bounds on the conductor and the coefficients on a minimal Weierstrass equation. In total we considered around 20.0 million of abelian surfaces of which 49.16% have a Tate-Shafarevich group of non-square order.