Invariants
| Level: | $90$ | $\SL_2$-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: | $4$ (of which $2$ are rational) | Cusp widths | $18^{2}\cdot90^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $16$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 13$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 13$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 90E13 |
Level structure
| $\GL_2(\Z/90\Z)$-generators: | $\begin{bmatrix}11&20\\68&73\end{bmatrix}$, $\begin{bmatrix}37&81\\33&20\end{bmatrix}$, $\begin{bmatrix}44&73\\67&70\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 90-isogeny field degree: | $36$ |
| Cyclic 90-torsion field degree: | $864$ |
| Full 90-torsion field degree: | $51840$ |
Rational points
This modular curve has 2 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 |
|---|---|---|---|---|---|
| 30.72.1.o.1 | $30$ | $3$ | $3$ | $1$ | $1$ |
| 45.108.6.a.2 | $45$ | $2$ | $2$ | $6$ | $1$ |
| 90.108.4.f.2 | $90$ | $2$ | $2$ | $4$ | $?$ |
| 90.108.7.bj.1 | $90$ | $2$ | $2$ | $7$ | $?$ |