2 problems

Let $f$ be a weight-$2$ newform of level $\Gamma_0(p)$ with integer Fourier coefficients, let $E=E_f$ be the associated elliptic curve with multiplicative reduction at $p$, and let…

Algebraicity conjecture. If $r_{\mathrm{alg}}(A/E)\geq r$, then there exists $w_{A,S}\in\bigwedge^r(A(E)_{\mathbb Q})$ such that