Invariants
| Level: | $240$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2^{3}\cdot5^{2}\cdot10^{3}\cdot16\cdot80$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 80H7 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}4&193\\47&70\end{bmatrix}$, $\begin{bmatrix}17&90\\188&119\end{bmatrix}$, $\begin{bmatrix}52&9\\159&142\end{bmatrix}$, $\begin{bmatrix}98&15\\231&202\end{bmatrix}$, $\begin{bmatrix}123&20\\172&91\end{bmatrix}$, $\begin{bmatrix}130&159\\73&56\end{bmatrix}$, $\begin{bmatrix}216&95\\137&54\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.144.7.um.2 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 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 |
|---|---|---|---|---|---|
| 80.144.3-40.bx.1.18 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-40.bx.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 240.48.0-240.n.2.2 | $240$ | $6$ | $6$ | $0$ | $?$ |