Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | 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 | $4^{8}\cdot8^{4}\cdot16^{2}$ | 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: | 16I2 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}1&64\\60&59\end{bmatrix}$, $\begin{bmatrix}9&16\\44&15\end{bmatrix}$, $\begin{bmatrix}49&28\\12&33\end{bmatrix}$, $\begin{bmatrix}55&16\\48&23\end{bmatrix}$, $\begin{bmatrix}63&60\\52&53\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.96.2.g.1 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $24$ |
| Cyclic 80-torsion field degree: | $384$ |
| Full 80-torsion field degree: | $61440$ |
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 |
|---|---|---|---|---|---|
| 16.96.0-8.c.1.3 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 40.96.0-8.c.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.