Bounding the 𝑗-invariant of integral points on 𝑋_{𝑛𝑠}⁺(𝑝)

Bajolet, Aurélien; Sha, Min

doi:10.1090/S0002-9939-2014-12100-9

Bounding the $j$-invariant of integral points on $X_{\mathrm {ns}}^{+}(p)$
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by Aurélien Bajolet and Min Sha PDF

Proc. Amer. Math. Soc. 142 (2014), 3395-3410 Request permission

Abstract:

For any prime $p\ge 7$, by using Baker’s method we obtain two explicit bounds in terms of $p$ for the $j$-invariant of an integral point on $X_{\mathrm {ns}}^{+}(p)$ which is the modular curve of level $p$ corresponding to the normalizer of a non-split Cartan subgroup of $\mathrm {GL}_2(\mathbb {Z}/p\mathbb {Z})$.

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