Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{6}\cdot24^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24W7 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}55&52\\4&87\end{bmatrix}$, $\begin{bmatrix}55&98\\32&47\end{bmatrix}$, $\begin{bmatrix}63&80\\28&33\end{bmatrix}$, $\begin{bmatrix}75&82\\64&65\end{bmatrix}$, $\begin{bmatrix}107&100\\0&79\end{bmatrix}$, $\begin{bmatrix}109&70\\88&21\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.7.yz.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.3-24.e.1.6 | $24$ | $2$ | $2$ | $3$ | $1$ |
| 120.144.3-24.e.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.4-120.bm.2.42 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.bm.2.94 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.bo.1.101 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.bo.1.123 | $120$ | $2$ | $2$ | $4$ | $?$ |