Invariants
| Level: | $120$ | $\SL_2$-level: | $30$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot10^{2}\cdot30^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 30N5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}20&87\\77&10\end{bmatrix}$, $\begin{bmatrix}29&45\\41&88\end{bmatrix}$, $\begin{bmatrix}97&21\\0&103\end{bmatrix}$, $\begin{bmatrix}98&115\\15&103\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.5.ey.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has no $\Q_p$ points for $p=41$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 60.96.1-60.bx.2.14 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.96.1-60.bx.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.3-120.c.1.4 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.96.3-120.c.1.15 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.96.3-120.cu.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.96.3-120.cu.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ |