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Complete verification of strong BSD for many modular abelian surfaces over $\mathbf{Q}$
We develop the theory and algorithms necessary to be able to verify the strong Birch--Swinnerton-Dyer Conjecture for absolutely simple modular abelian varieties over $\mathbf{Q}$. We apply our methods to all 28 Atkin--Lehner quotients of $X_0(N)$ of genus $2$, all 97 genus $2$ curves from the LMFDB
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