Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $5^{4}\cdot10^{2}\cdot40^{2}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40G7 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}28&5\\25&28\end{bmatrix}$, $\begin{bmatrix}70&117\\103&52\end{bmatrix}$, $\begin{bmatrix}88&75\\25&38\end{bmatrix}$, $\begin{bmatrix}89&10\\70&9\end{bmatrix}$, $\begin{bmatrix}102&83\\5&8\end{bmatrix}$, $\begin{bmatrix}109&82\\26&21\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.120.7.cv.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $147456$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(5)$ | $5$ | $24$ | $12$ | $0$ | $0$ |
| 24.24.0-24.z.1.6 | $24$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.24.0-24.z.1.6 | $24$ | $10$ | $10$ | $0$ | $0$ |
| 40.120.3-20.c.1.5 | $40$ | $2$ | $2$ | $3$ | $0$ |
| 120.120.3-20.c.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.