Date:

Thu, 21/04/201614:00-15:15

Location:

TBA

In this talk we present a database of rational elliptic curves with

good reduction outside certain finite sets of primes, including the

set {2, 3, 5, 7, 11}, and all sets whose product is at most 1000.

In fact this is a biproduct of a larger project, in which we construct

practical algorithms to solve S-unit, Mordell, cubic Thue, cubic

Thue--Mahler, as well as generalized Ramanujan--Nagell equations, and

to compute S-integral points on rational elliptic curves with given

Mordell--Weil basis.

Our algorithms rely on new height bounds, which we obtained using the

method of Faltings (Arakelov, Parshin, Szpiro) combined with the

Shimura--Taniyama conjecture (without relying on linear forms in

logarithms), as well as several improved and new sieves.

In addition we used the resulting data to motivate several conjectures

and questions, such as Baker's explicit abc-conjecture, and a new

conjecture on the number of S-integral points of rational elliptic

curves.

This is joint work with Rafael von Känel.

good reduction outside certain finite sets of primes, including the

set {2, 3, 5, 7, 11}, and all sets whose product is at most 1000.

In fact this is a biproduct of a larger project, in which we construct

practical algorithms to solve S-unit, Mordell, cubic Thue, cubic

Thue--Mahler, as well as generalized Ramanujan--Nagell equations, and

to compute S-integral points on rational elliptic curves with given

Mordell--Weil basis.

Our algorithms rely on new height bounds, which we obtained using the

method of Faltings (Arakelov, Parshin, Szpiro) combined with the

Shimura--Taniyama conjecture (without relying on linear forms in

logarithms), as well as several improved and new sieves.

In addition we used the resulting data to motivate several conjectures

and questions, such as Baker's explicit abc-conjecture, and a new

conjecture on the number of S-integral points of rational elliptic

curves.

This is joint work with Rafael von Känel.