论文标题
$ x_1（\ ell^n）$的隔离点，带有理性$ j $ -invariant}
Isolated Points on $X_1(\ell^n)$ with rational $j$-invariant}
论文作者
论文摘要
令$ \ ell $为素数，让$ n \ geq 1 $。 In this note we show that if there is a non-cuspidal, non-CM isolated point $x$ with a rational $j$-invariant on the modular curve $X_1(\ell^n)$, then $\ell=37$ and the $j$-invariant of $x$ is either $7\cdot11^3$ or $-7.137^3\cdot2083^3$.相反的含义对第一个J-Invariant具有，但目前尚不清楚它是否存在第二个。
Let $\ell$ be a prime and let $n\geq 1$. In this note we show that if there is a non-cuspidal, non-CM isolated point $x$ with a rational $j$-invariant on the modular curve $X_1(\ell^n)$, then $\ell=37$ and the $j$-invariant of $x$ is either $7\cdot11^3$ or $-7.137^3\cdot2083^3$. The reverse implication holds for the first j-invariant but it is currently unknown whether or not it holds for the second.
