6 problems

Zywina's refined Koblitz conjecture.

The CM Koblitz conjecture in arithmetic progressions. There exists a constant $C_{E/K,n,k}^{\operatorname{prime}}$ such that

Let $E$ be an elliptic curve defined over the rational number field $\mathbb{Q}$, let $\Delta$ be its discriminant, and let $t\geq 1$ be a positive integer. Define $\pi(x,E,t)$ to…

Let $E$ be the elliptic curve over $\mathbb Q$ defined by $y^2=x^3-x$, with complex multiplication by $\mathbb Z[i]$, and let $\mathcal C_{E_{\mathbb Q(i)},8}$ be the refined Kobli…

Let $K$ be a number field, let $E$ be an elliptic curve over $K$, and let $t$ be a positive integer. Let $S_E$ be the set of primes of bad reduction, let $\Sigma_K(x)$ denote the p…

Let $K$ be a number field, let $E$ be an elliptic curve over $K$, and let $S_E$ be its set of primes of bad reduction. For a positive integer $t$, and for each prime ideal…