Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 8 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{4}\cdot40^{4}$ | Cusp orbits | $4^{2}$ | ||
| Elliptic points: | $8$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 28$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 15$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40I15 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}0&67\\77&80\end{bmatrix}$, $\begin{bmatrix}10&57\\17&50\end{bmatrix}$, $\begin{bmatrix}31&96\\44&17\end{bmatrix}$, $\begin{bmatrix}81&112\\88&19\end{bmatrix}$, $\begin{bmatrix}98&81\\69&14\end{bmatrix}$, $\begin{bmatrix}102&1\\53&58\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| 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 $p=13$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.7.jq.1 | $40$ | $2$ | $2$ | $7$ | $4$ |
| 60.120.7.jx.1 | $60$ | $2$ | $2$ | $7$ | $3$ |
| 120.24.0.oj.1 | $120$ | $10$ | $10$ | $0$ | $?$ |
| 120.120.7.bfw.1 | $120$ | $2$ | $2$ | $7$ | $?$ |