Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4$ | ||
| 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: | 16I3 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}13&40\\68&41\end{bmatrix}$, $\begin{bmatrix}41&64\\31&63\end{bmatrix}$, $\begin{bmatrix}49&48\\67&11\end{bmatrix}$, $\begin{bmatrix}57&16\\5&31\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.96.3.gl.1 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $12$ |
| Cyclic 80-torsion field degree: | $96$ |
| Full 80-torsion field degree: | $61440$ |
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 |
|---|---|---|---|---|---|
| 16.96.0-16.j.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 80.96.0-16.j.1.8 | $80$ | $2$ | $2$ | $0$ | $?$ |
| 40.96.1-40.cy.1.2 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 80.96.1-40.cy.1.6 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 80.96.2-80.j.1.1 | $80$ | $2$ | $2$ | $2$ | $?$ |
| 80.96.2-80.j.1.4 | $80$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 80.384.5-80.lo.1.2 | $80$ | $2$ | $2$ | $5$ |
| 80.384.5-80.lo.2.3 | $80$ | $2$ | $2$ | $5$ |
| 80.384.5-80.lq.1.1 | $80$ | $2$ | $2$ | $5$ |
| 80.384.5-80.lq.2.1 | $80$ | $2$ | $2$ | $5$ |
| 160.384.7-160.cj.1.12 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.cm.1.10 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.cy.1.8 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.cz.1.4 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.ee.1.2 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.ef.1.4 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.er.1.2 | $160$ | $2$ | $2$ | $7$ |
| 160.384.7-160.eu.1.4 | $160$ | $2$ | $2$ | $7$ |
| 240.384.5-240.bra.1.3 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bra.2.5 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.brc.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.brc.2.1 | $240$ | $2$ | $2$ | $5$ |