Posted in

Speaker:

Eleni Agathocleous
Affiliation:

MPIM
Date:

Wed, 17/07/2024 - 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar In this talk I will discuss recent results concerning the rank of an infinite family of elliptic

curves of $j$-invariant zero. I will describe an explicit relation between the 3-Selmer group

of these elliptic curves, and the 3-Selmer group of quadratic number fields with non-trivial

3-class group. By combining with results of T. Honda and Ph. Satgé, I will show how I

derived lower and upper bounds for the rank of these elliptic curves through the method of

descent, and by assuming finiteness of the Tate-Shafarevich group. Finally, I will describe

the torsors for these curves, and give a new example of genus-1 curves that violate the Hasse

Principle.

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