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For an optimal modular parametrization $J_0(n) \twoheadrightarrow E$ of anelliptic curve $E$ over $\mathbb{Q}$ of conductor $n$, Manin conjectured theagreement of two natural $\mathbb{Z}$-lattices in the $\mathbb{Q}$-vector space$H^0(E, \Omega^1)$. Multiple authors generalized his conjecture to higherdimensional newform quotients. We prove the Manin conjecture for semistable$E$, give counterexamples to all the proposed generalizations, and proveseveral semistable special cases of these generalizations. The proofs establishgeneral relations between the integral $p$-adic etale and de Rham cohomologiesof abelian varieties over $p$-adic fields and exhibit a new exactness resultfor Neron models.

The Manin constant in the semistable case