Invariants
Level: | $160$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $3 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $4^{2}\cdot8\cdot32$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 32B3 |
Level structure
$\GL_2(\Z/160\Z)$-generators: | $\begin{bmatrix}41&72\\120&137\end{bmatrix}$, $\begin{bmatrix}50&3\\81&8\end{bmatrix}$, $\begin{bmatrix}79&14\\6&55\end{bmatrix}$, $\begin{bmatrix}130&91\\147&34\end{bmatrix}$, $\begin{bmatrix}133&144\\54&91\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 160.48.3.e.1 for the level structure with $-I$) |
Cyclic 160-isogeny field degree: | $24$ |
Cyclic 160-torsion field degree: | $768$ |
Full 160-torsion field degree: | $1966080$ |
Rational points
This modular curve has 4 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 |
---|---|---|---|---|---|
16.48.1-16.b.1.2 | $16$ | $2$ | $2$ | $1$ | $0$ |
160.48.1-16.b.1.1 | $160$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.