Invariants
| Level: | $180$ | $\SL_2$-level: | $36$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $5 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{6}\cdot4^{6}\cdot18^{2}\cdot36^{2}$ | Cusp orbits | $2^{6}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 36L5 |
Level structure
| $\GL_2(\Z/180\Z)$-generators: | $\begin{bmatrix}61&150\\8&149\end{bmatrix}$, $\begin{bmatrix}65&102\\81&79\end{bmatrix}$, $\begin{bmatrix}157&6\\54&131\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 180.144.5.x.1 for the level structure with $-I$) |
| Cyclic 180-isogeny field degree: | $12$ |
| Cyclic 180-torsion field degree: | $576$ |
| Full 180-torsion field degree: | $622080$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 36.144.1-36.g.1.4 | $36$ | $2$ | $2$ | $1$ | $0$ |
| 60.96.1-60.x.1.1 | $60$ | $3$ | $3$ | $1$ | $0$ |
| 180.144.1-180.d.1.1 | $180$ | $2$ | $2$ | $1$ | $?$ |
| 180.144.1-180.d.1.8 | $180$ | $2$ | $2$ | $1$ | $?$ |
| 180.144.1-36.g.1.8 | $180$ | $2$ | $2$ | $1$ | $?$ |
| 180.144.3-180.bf.1.8 | $180$ | $2$ | $2$ | $3$ | $?$ |
| 180.144.3-180.bf.1.12 | $180$ | $2$ | $2$ | $3$ | $?$ |