Invariants
| Level: | $220$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $160$ | $\PSL_2$-index: | $160$ | ||||
| Genus: | $9 = 1 + \frac{ 160 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{8}$ | Cusp orbits | $8$ | ||
| Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A9 |
Level structure
| $\GL_2(\Z/220\Z)$-generators: | $\begin{bmatrix}73&65\\78&147\end{bmatrix}$, $\begin{bmatrix}102&5\\55&27\end{bmatrix}$, $\begin{bmatrix}219&18\\122&141\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 220-isogeny field degree: | $432$ |
| Cyclic 220-torsion field degree: | $34560$ |
| Full 220-torsion field degree: | $3801600$ |
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 |
|---|---|---|---|---|---|
| 20.80.3.b.1 | $20$ | $2$ | $2$ | $3$ | $2$ |
| 110.40.1.k.1 | $110$ | $4$ | $4$ | $1$ | $?$ |
| 220.80.5.c.1 | $220$ | $2$ | $2$ | $5$ | $?$ |
| 220.80.5.e.1 | $220$ | $2$ | $2$ | $5$ | $?$ |