Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}\cdot12^{4}\cdot24^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AC9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}33&62\\34&97\end{bmatrix}$, $\begin{bmatrix}38&107\\111&70\end{bmatrix}$, $\begin{bmatrix}49&54\\54&97\end{bmatrix}$, $\begin{bmatrix}79&84\\104&83\end{bmatrix}$, $\begin{bmatrix}89&72\\72&77\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.9.bfp.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $92160$ |
Rational points
This modular curve has no $\Q_p$ points for $p=37$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.5-24.bh.2.22 | $24$ | $2$ | $2$ | $5$ | $0$ |
| 60.192.3-60.bh.1.2 | $60$ | $2$ | $2$ | $3$ | $1$ |
| 120.192.3-60.bh.1.35 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.kh.1.30 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.kh.1.37 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.5-24.bh.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ |