Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8G0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&52\\76&107\end{bmatrix}$, $\begin{bmatrix}9&64\\98&115\end{bmatrix}$, $\begin{bmatrix}17&8\\102&41\end{bmatrix}$, $\begin{bmatrix}43&8\\34&93\end{bmatrix}$, $\begin{bmatrix}83&36\\6&11\end{bmatrix}$, $\begin{bmatrix}95&56\\88&105\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.24.0.y.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $737280$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-4.b.1.4 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 120.24.0-4.b.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.z.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.z.1.32 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.ba.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.ba.1.32 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.