Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $5 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{12}$ | Cusp orbits | $4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10B5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&44\\38&69\end{bmatrix}$, $\begin{bmatrix}35&46\\34&15\end{bmatrix}$, $\begin{bmatrix}35&52\\12&79\end{bmatrix}$, $\begin{bmatrix}47&66\\18&113\end{bmatrix}$, $\begin{bmatrix}73&54\\14&61\end{bmatrix}$, $\begin{bmatrix}109&60\\10&109\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.120.5.b.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $147456$ |
Rational points
This modular curve has no $\Q_p$ points for $p=13,17$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.3-10.a.1.2 | $40$ | $2$ | $2$ | $3$ | $0$ |
| 60.120.3-10.a.1.3 | $60$ | $2$ | $2$ | $3$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.