Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{16}\cdot16^{8}$ | Cusp orbits | $2^{6}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M5 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}33&32\\65&3\end{bmatrix}$, $\begin{bmatrix}37&40\\30&21\end{bmatrix}$, $\begin{bmatrix}57&16\\38&37\end{bmatrix}$, $\begin{bmatrix}69&24\\60&17\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.192.5.lq.2 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $6$ |
| Cyclic 80-torsion field degree: | $48$ |
| Full 80-torsion field degree: | $30720$ |
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 |
|---|---|---|---|---|---|
| 16.192.1-16.m.2.3 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 40.192.1-40.cm.2.1 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 80.192.1-16.m.2.9 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 80.192.1-80.bg.1.1 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 80.192.1-80.bg.1.4 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 80.192.1-40.cm.2.7 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 80.192.3-80.gl.1.1 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.192.3-80.gl.1.4 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.192.3-80.hd.1.1 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.192.3-80.hd.1.2 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.192.3-80.he.2.5 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.192.3-80.he.2.9 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.192.3-80.hf.1.6 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.192.3-80.hf.1.11 | $80$ | $2$ | $2$ | $3$ | $?$ |