Root numbers and parity of local Iwasawa invariants
  Given two elliptic curves $E_1$ and $E_2$ defined over the field of rational numbers, $\mathbb{Q}$, with good reduction at an odd prime $p$ and equivalent mod $p$ Galois representation, we compare the $p$-Selmer rank, global and local root numbers of $E_1$ and $E_2$ over number fields. 
Suman Ahmed, Chandrakant Aribam, Sudhanshu Shekhar
math.NT