Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $4\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16I3 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}19&10\\50&73\end{bmatrix}$, $\begin{bmatrix}27&70\\16&57\end{bmatrix}$, $\begin{bmatrix}61&66\\72&71\end{bmatrix}$, $\begin{bmatrix}67&56\\29&29\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 80.192.3-80.ue.1.1, 80.192.3-80.ue.1.2, 80.192.3-80.ue.1.3, 80.192.3-80.ue.1.4, 160.192.3-80.ue.1.1, 160.192.3-80.ue.1.2, 240.192.3-80.ue.1.1, 240.192.3-80.ue.1.2, 240.192.3-80.ue.1.3, 240.192.3-80.ue.1.4 |
| Cyclic 80-isogeny field degree: | $48$ |
| Cyclic 80-torsion field degree: | $1536$ |
| Full 80-torsion field degree: | $122880$ |
Rational points
This modular curve has no $\Q_p$ points for $p=3$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.48.1.bb.1 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 40.48.1.jd.1 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 80.48.0.cp.2 | $80$ | $2$ | $2$ | $0$ | $?$ |
| 80.48.1.gn.1 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 80.48.2.ch.1 | $80$ | $2$ | $2$ | $2$ | $?$ |
| 80.48.2.cz.1 | $80$ | $2$ | $2$ | $2$ | $?$ |
| 80.48.2.ev.1 | $80$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 160.192.7.my.1 | $160$ | $2$ | $2$ | $7$ |
| 160.192.7.mz.1 | $160$ | $2$ | $2$ | $7$ |
| 240.288.19.byzx.1 | $240$ | $3$ | $3$ | $19$ |
| 240.384.21.iyz.1 | $240$ | $4$ | $4$ | $21$ |