Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $8^{16}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16B7 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}9&80\\148&239\end{bmatrix}$, $\begin{bmatrix}97&4\\168&113\end{bmatrix}$, $\begin{bmatrix}105&164\\16&111\end{bmatrix}$, $\begin{bmatrix}153&160\\236&201\end{bmatrix}$, $\begin{bmatrix}201&28\\112&139\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.192.7.hi.1 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $96$ |
| Cyclic 240-torsion field degree: | $1536$ |
| Full 240-torsion field degree: | $1474560$ |
Rational points
This modular curve has no $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 48.192.2-48.c.1.1 | $48$ | $2$ | $2$ | $2$ | $0$ |
| 80.192.2-80.g.1.1 | $80$ | $2$ | $2$ | $2$ | $?$ |
| 120.192.3-120.cw.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.2-48.c.1.10 | $240$ | $2$ | $2$ | $2$ | $?$ |
| 240.192.2-80.g.1.28 | $240$ | $2$ | $2$ | $2$ | $?$ |
| 240.192.3-120.cw.1.4 | $240$ | $2$ | $2$ | $3$ | $?$ |