Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M1 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}7&0\\65&19\end{bmatrix}$, $\begin{bmatrix}47&16\\194&209\end{bmatrix}$, $\begin{bmatrix}65&24\\234&193\end{bmatrix}$, $\begin{bmatrix}123&64\\182&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.96.1.wo.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $48$ |
| Cyclic 240-torsion field degree: | $1536$ |
| Full 240-torsion field degree: | $2949120$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.96.0-40.bj.2.2 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 240.96.0-40.bj.2.7 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 48.96.0-48.bf.1.15 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 240.96.0-48.bf.1.9 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.96.0-240.bi.1.5 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.96.0-240.bi.1.30 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.96.0-240.ej.1.13 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.96.0-240.ej.1.19 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.96.1-240.gb.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gb.1.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gh.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gh.1.26 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.go.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.go.1.27 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |