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: | $\begin{bmatrix}5&216\\18&85\end{bmatrix}$, $\begin{bmatrix}93&104\\160&29\end{bmatrix}$, $\begin{bmatrix}193&112\\62&69\end{bmatrix}$, $\begin{bmatrix}197&24\\165&187\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.192.5.bqx.1 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 |
|---|---|---|---|---|---|
| 48.192.3-48.fj.1.2 | $48$ | $2$ | $2$ | $3$ | $1$ |
| 80.192.1-80.bf.1.3 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.ql.2.15 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-80.bf.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-240.dn.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-240.dn.2.18 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-120.ql.2.8 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.3-48.fj.1.3 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rm.1.8 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rm.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rn.2.6 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.rn.2.26 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.ro.1.5 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.ro.1.6 | $240$ | $2$ | $2$ | $3$ | $?$ |