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 | $2^{6}\cdot4\cdot8$ | ||
| 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: | $\begin{bmatrix}21&8\\23&155\end{bmatrix}$, $\begin{bmatrix}149&168\\10&113\end{bmatrix}$, $\begin{bmatrix}169&96\\77&139\end{bmatrix}$, $\begin{bmatrix}229&152\\211&79\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.192.5.brd.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 no $\Q_p$ points for $p=29$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.192.1-16.l.2.2 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 120.192.1-120.qp.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-16.l.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-240.do.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-240.do.1.22 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.1-120.qp.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.3-240.qk.1.2 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.qk.1.13 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.sa.1.2 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.sa.1.31 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.sc.1.9 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.sc.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.sk.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ |
| 240.192.3-240.sk.2.4 | $240$ | $2$ | $2$ | $3$ | $?$ |