Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $13 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $5^{8}\cdot10^{4}\cdot40^{4}$ | Cusp orbits | $4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 13$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40G13 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}31&22\\58&59\end{bmatrix}$, $\begin{bmatrix}76&101\\67&54\end{bmatrix}$, $\begin{bmatrix}96&109\\61&40\end{bmatrix}$, $\begin{bmatrix}103&100\\30&73\end{bmatrix}$, $\begin{bmatrix}108&95\\5&58\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.13.bzw.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=13,17,83$, and therefore no 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 |
|---|---|---|---|---|---|
| 5.20.0.b.1 | $5$ | $24$ | $12$ | $0$ | $0$ |
| 24.24.0-24.ba.1.12 | $24$ | $20$ | $20$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.240.5-20.m.1.3 | $40$ | $2$ | $2$ | $5$ | $0$ |
| 60.240.5-20.m.1.4 | $60$ | $2$ | $2$ | $5$ | $0$ |
| 120.120.4-120.cc.1.4 | $120$ | $4$ | $4$ | $4$ | $?$ |
| 120.240.7-120.db.1.11 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.db.1.21 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.39 | $120$ | $2$ | $2$ | $7$ | $?$ |