Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $6^{2}\cdot12^{3}\cdot24$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24G4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&118\\28&7\end{bmatrix}$, $\begin{bmatrix}25&2\\116&57\end{bmatrix}$, $\begin{bmatrix}49&80\\68&77\end{bmatrix}$, $\begin{bmatrix}65&86\\84&37\end{bmatrix}$, $\begin{bmatrix}69&74\\68&77\end{bmatrix}$, $\begin{bmatrix}91&2\\116&105\end{bmatrix}$, $\begin{bmatrix}107&114\\56&73\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.4.bo.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.72.2-12.b.1.6 | $12$ | $2$ | $2$ | $2$ | $0$ |
| 120.72.2-12.b.1.19 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.48.0-120.u.1.51 | $120$ | $3$ | $3$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.