Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $8^{8}\cdot16^{8}$ | Cusp orbits | $1^{4}\cdot2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16E9 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}17&206\\128&43\end{bmatrix}$, $\begin{bmatrix}25&146\\152&131\end{bmatrix}$, $\begin{bmatrix}137&80\\224&69\end{bmatrix}$, $\begin{bmatrix}153&166\\136&223\end{bmatrix}$, $\begin{bmatrix}185&222\\16&191\end{bmatrix}$, $\begin{bmatrix}233&78\\56&115\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.192.9.bja.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 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.192.1-8.g.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 240.192.1-8.g.2.12 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.192.5-240.cw.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.cw.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.cx.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.cx.1.47 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.ec.2.2 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.ec.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.eo.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.eo.1.32 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.gx.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.gx.1.24 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.ha.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ |
| 240.192.5-240.ha.1.13 | $240$ | $2$ | $2$ | $5$ | $?$ |