论文标题
$ x_1（n）$的奇数隔离点，有理$ j $ - invariant
Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
论文作者
论文摘要
令$ c $为在数字字段$ k $上定义的曲线。我们说，如果$ d $的c $ of $ d $的闭合点$ x \如果它不属于由投影线的参数或正等级的曲线Jacobian的ABELIAN ABELIAN SUBVARIETION参数的无限族家族。在Bourdon，Ejder，Liu，Odumodu和Viray的作品的基础上，我们以合理的$ J $ -INVARIANT进行了椭圆曲线的特征，从而在$ x_1（n）/\ mathbb {q} $上引起了奇数奇数的孤立点，以获得一些正integer $ n $。
Let $C$ be a curve defined over a number field $k$. We say a closed point $x\in C$ of degree $d$ is isolated if it does not belong to an infinite family of degree $d$ points parametrized by the projective line or a positive rank abelian subvariety of the curve's Jacobian. Building on work of Bourdon, Ejder, Liu, Odumodu, and Viray, we characterize elliptic curves with rational $j$-invariant which give rise to an isolated point of odd degree on $X_1(N)/\mathbb{Q}$ for some positive integer $N$.
