Isolated points on $$X_1(\ell ^n)$$ with rational j-invariant
نویسندگان
چکیده
Let $$\ell $$ be a prime and let $$n\ge 1$$ . In this note we show that if there is non-cuspidal, non-CM isolated point x with rational j-invariant on the modular curve $$X_1(\ell ^n)$$ , then =37$$ of either $$7\cdot 11^3$$ or $$-7.137^3\cdot 2083^3$$ The reverse implication holds for first but it currently unknown whether not second.
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ژورنال
عنوان ژورنال: Research in number theory
سال: 2022
ISSN: ['2363-9555', '2522-0160']
DOI: https://doi.org/10.1007/s40993-022-00313-0