Invariants
| Level: | $240$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot10^{2}\cdot16\cdot20\cdot80$ | Cusp orbits | $1^{8}$ | ||
| 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: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 80E9 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}18&11\\109&220\end{bmatrix}$, $\begin{bmatrix}89&174\\100&143\end{bmatrix}$, $\begin{bmatrix}162&19\\49&152\end{bmatrix}$, $\begin{bmatrix}198&59\\65&212\end{bmatrix}$, $\begin{bmatrix}212&51\\71&32\end{bmatrix}$, $\begin{bmatrix}234&25\\61&118\end{bmatrix}$, $\begin{bmatrix}238&135\\239&134\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.144.9.blw.1 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $8$ |
| Cyclic 240-torsion field degree: | $256$ |
| Full 240-torsion field degree: | $1966080$ |
Rational points
This modular curve has 8 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 |
|---|---|---|---|---|---|
| 80.144.3-40.bx.1.18 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-40.bx.1.37 | $120$ | $2$ | $2$ | $3$ | $?$ |