L. Szymaszkiewicz

activity

20182021

collaborators

4 papers

math.NT2021

Critical $L$ -values of Gross curves

Andrzej Dąbrowski, Tomasz Jędrzejak, Lucjan Szymaszkiewicz

Let $K = Q (- q)$ , where $q$ is a prime congruent to $3$ modulo $4$ . Let $A = A (q)$ denote the Gross curve over the Hilbert class field $H$ of $K$ . In this note we use…

math.NT2021

Elliptic curves with exceptionally large analytic order of the Tate-Shafarevich groups

Andrzej Dąbrowski, Lucjan Szymaszkiewicz

We exhibit $88$ examples of rank zero elliptic curves over the rationals with $|\sza(E)| > 63408^2$, which was the largest previously known value for any explicit curve. Our record…

math.NT2019

Critical $L$ -values for some quadratic twists of Gross curves

Andrzej Dąbrowski, Tomasz Jędrzejak, Lucjan Szymaszkiewicz

Let $K = Q (- q)$ , where $q$ is a prime congruent to $3$ modulo $4$ . Let $A = A (q)$ denote the Gross curve. Let $E = A^{(- β)}$ denote its quadratic twist, with $β = - q$ . T…

math.NT2018

Orders of Tate-Shafarevich groups for the cubic twists of $X_{0} (27)$

Andrzej Dąbrowski, Lucjan Szymaszkiewicz

This paper continues the authors previous investigations concerning orders of Tate-Shafarevich groups in quadratic twists of a given elliptic curve, and for the family of the Neuma…

Critical L-values of Gross curves

Elliptic curves with exceptionally large analytic order of the Tate-Shafarevich groups

Critical L-values for some quadratic twists of Gross curves

Orders of Tate-Shafarevich groups for the cubic twists of X0​(27)

Critical $L$ -values of Gross curves

Critical $L$ -values for some quadratic twists of Gross curves

Orders of Tate-Shafarevich groups for the cubic twists of $X_{0} (27)$