| Curve name | $X_{1}$ |
| Index | $1$ |
| Level | $1$ |
| Genus | $0$ |
| Does the subgroup contain $-I$? | Yes |
| Generating matrices | |
| Images in lower levels | |
| Meaning/Special name | $X(1)$ |
| Chosen covering | |
| Curves that $X_{1}$ minimally covers | |
| Curves that minimally cover $X_{1}$ | $X_{2}$, $X_{3}$, $X_{4}$, $X_{5}$, $X_{6}$, $X_{7}$ |
| Curves that minimally cover $X_{1}$ and have infinitely many rational points. | $X_{2}$, $X_{3}$, $X_{4}$, $X_{5}$, $X_{6}$, $X_{7}$ |
| Model | $\mathbb{P}^{1} \cong \mathbb{Q}(f_{1})$, where $f_{1} = j$ |
| Info about rational points | None |
| Comments on finding rational points | None |
| Elliptic curve whose $2$-adic image is the subgroup | $y^2 + y = x^3 - x^2 - 10x - 20$, with conductor $11$ |
| Generic density of odd order reductions | $11/21$ |