Invariants
| Level: | $90$ | $\SL_2$-level: | $18$ | Newform level: | $1$ | ||
| Index: | $162$ | $\PSL_2$-index: | $162$ | ||||
| Genus: | $10 = 1 + \frac{ 162 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 9 }{2}$ | ||||||
| Cusps: | $9$ (none of which are rational) | Cusp widths | $18^{9}$ | Cusp orbits | $3\cdot6$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 18$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 10$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 18A10 |
Level structure
| $\GL_2(\Z/90\Z)$-generators: | $\begin{bmatrix}3&38\\53&79\end{bmatrix}$, $\begin{bmatrix}89&14\\21&53\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 90-isogeny field degree: | $72$ |
| Cyclic 90-torsion field degree: | $1728$ |
| Full 90-torsion field degree: | $69120$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 9.27.0.a.1 | $9$ | $6$ | $6$ | $0$ | $0$ |
| 10.6.0.a.1 | $10$ | $27$ | $27$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.6.0.a.1 | $10$ | $27$ | $27$ | $0$ | $0$ |
| 18.81.4.a.1 | $18$ | $2$ | $2$ | $4$ | $0$ |
| 90.54.2.a.1 | $90$ | $3$ | $3$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 180.324.22.y.1 | $180$ | $2$ | $2$ | $22$ |
| 180.324.22.ba.1 | $180$ | $2$ | $2$ | $22$ |
| 180.324.22.ca.1 | $180$ | $2$ | $2$ | $22$ |
| 180.324.22.cc.1 | $180$ | $2$ | $2$ | $22$ |
| 180.324.22.fe.1 | $180$ | $2$ | $2$ | $22$ |
| 180.324.22.fg.1 | $180$ | $2$ | $2$ | $22$ |
| 180.324.22.fm.1 | $180$ | $2$ | $2$ | $22$ |
| 180.324.22.fo.1 | $180$ | $2$ | $2$ | $22$ |