Invariants
| Level: | $180$ | $\SL_2$-level: | $90$ | Newform level: | $1$ | ||
| Index: | $216$ | $\PSL_2$-index: | $216$ | ||||
| Genus: | $13 = 1 + \frac{ 216 }{12} - \frac{ 16 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $18^{2}\cdot90^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $16$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 13$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 90E13 |
Level structure
| $\GL_2(\Z/180\Z)$-generators: | $\begin{bmatrix}43&144\\141&131\end{bmatrix}$, $\begin{bmatrix}59&99\\72&101\end{bmatrix}$, $\begin{bmatrix}73&94\\91&71\end{bmatrix}$, $\begin{bmatrix}133&15\\177&166\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 180-isogeny field degree: | $72$ |
| Cyclic 180-torsion field degree: | $3456$ |
| Full 180-torsion field degree: | $829440$ |
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 |
|---|---|---|---|---|---|
| 60.72.1.fo.1 | $60$ | $3$ | $3$ | $1$ | $1$ |
| 90.108.4.g.2 | $90$ | $2$ | $2$ | $4$ | $?$ |
| 180.108.6.h.2 | $180$ | $2$ | $2$ | $6$ | $?$ |
| 180.108.7.fd.1 | $180$ | $2$ | $2$ | $7$ | $?$ |