Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{16}\cdot16^{8}$ | Cusp orbits | $2^{4}\cdot4^{2}\cdot8$ | ||
| 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: | 16M5 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}13&120\\71&187\end{bmatrix}$, $\begin{bmatrix}17&224\\129&131\end{bmatrix}$, $\begin{bmatrix}61&152\\44&225\end{bmatrix}$, $\begin{bmatrix}117&136\\230&229\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.192.5.bra.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $48$ |
| Cyclic 240-torsion field degree: | $768$ |
| Full 240-torsion field degree: | $1474560$ |
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
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 48.192.1-48.bf.2.2 | $48$ | $2$ | $2$ | $1$ | $1$ |
| 80.192.3-80.gl.1.1 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.1-120.qn.2.13 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-48.bf.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-240.dn.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-240.dn.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-120.qn.2.8 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.3-80.gl.1.7 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rt.2.10 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rt.2.18 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.ru.1.2 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.ru.1.31 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rv.1.4 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rv.1.6 | $240$ | $2$ | $2$ | $3$ | $?$ |