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- W2905552162 abstract "Let $N=pq$ be a product of two distinct primes. There is an isogeny $J_0(N)^{rm new}to J^N$ defined over $mathbf{Q}$ between the new quotient of $J_0(N)$ and the Jacobian of the Shimura curve attached to the indefinite quaternion algebra of discriminant $N$. In the case when $p=2,3,5,7,13$, Ogg made predictions about the kernels of these isogenies. We show that Ogg's conjecture is not true in general. Afterwards, we propose a strategy for proving results toward Ogg's conjecture in certain situations. Finally, we discuss this strategy in detail for $N=5cdot 13$." @default.
- W2905552162 created "2018-12-22" @default.
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- W2905552162 date "2018-12-14" @default.
- W2905552162 modified "2023-09-27" @default.
- W2905552162 title "Galois extensions and a Conjecture of Ogg" @default.
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