Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24V3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}25&27\\106&119\end{bmatrix}$, $\begin{bmatrix}31&117\\118&29\end{bmatrix}$, $\begin{bmatrix}41&70\\32&9\end{bmatrix}$, $\begin{bmatrix}107&76\\68&63\end{bmatrix}$, $\begin{bmatrix}109&32\\10&27\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.3.tx.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has no $\Q_p$ points for $p=23$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.96.1-12.o.1.3 | $12$ | $2$ | $2$ | $1$ | $0$ |
| 120.96.1-12.o.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.2-120.k.1.24 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.96.2-120.k.1.33 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.96.2-120.r.1.32 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.96.2-120.r.1.41 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.384.9-120.bmk.1.5 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.bml.1.5 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.bms.1.9 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.bmt.1.6 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cer.1.13 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.ces.1.13 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cev.1.1 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cew.1.13 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cpt.1.9 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cpu.1.5 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cpx.1.5 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cpy.1.5 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cyr.1.1 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cys.1.14 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cyz.1.13 | $120$ | $2$ | $2$ | $9$ |
| 120.384.9-120.cza.1.13 | $120$ | $2$ | $2$ | $9$ |