Invariants
| Level: | $160$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
| Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot32^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 32B2 |
Level structure
| $\GL_2(\Z/160\Z)$-generators: | $\begin{bmatrix}41&16\\90&13\end{bmatrix}$, $\begin{bmatrix}57&96\\154&109\end{bmatrix}$, $\begin{bmatrix}85&24\\68&85\end{bmatrix}$, $\begin{bmatrix}117&72\\37&91\end{bmatrix}$, $\begin{bmatrix}141&104\\36&153\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 160.96.2.j.1 for the level structure with $-I$) |
| Cyclic 160-isogeny field degree: | $24$ |
| Cyclic 160-torsion field degree: | $384$ |
| Full 160-torsion field degree: | $983040$ |
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 |
|---|---|---|---|---|---|
| 16.96.0-16.j.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 160.96.0-16.j.1.2 | $160$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 160.384.5-160.cl.1.7 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.cl.2.4 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.cn.1.6 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.cn.2.6 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.ct.1.7 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.ct.2.3 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.cw.1.5 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.cw.2.3 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.ef.1.4 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.ef.2.4 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.eg.1.7 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.eg.2.7 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.et.1.3 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.et.2.2 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.ev.1.2 | $160$ | $2$ | $2$ | $5$ |
| 160.384.5-160.ev.2.3 | $160$ | $2$ | $2$ | $5$ |
| 160.384.7-160.cy.1.8 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.da.1.4 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.dg.1.6 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.di.1.6 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.ei.1.4 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.ej.1.8 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.es.1.2 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.eu.1.4 | $160$ | $2$ | $2$ | $7$ |