Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | 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: | $4$ (of which $2$ are rational) | Cusp widths | $8^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16B3 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}7&50\\36&23\end{bmatrix}$, $\begin{bmatrix}43&5\\52&41\end{bmatrix}$, $\begin{bmatrix}47&2\\72&59\end{bmatrix}$, $\begin{bmatrix}61&20\\20&17\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.48.3.bk.2 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $24$ |
| Cyclic 80-torsion field degree: | $768$ |
| Full 80-torsion field degree: | $122880$ |
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 |
|---|---|---|---|---|---|
| 8.48.1-8.n.1.4 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 80.48.1-8.n.1.4 | $80$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 80.192.5-80.ee.2.1 | $80$ | $2$ | $2$ | $5$ |
| 80.192.5-80.ef.2.9 | $80$ | $2$ | $2$ | $5$ |
| 80.192.5-80.ga.2.2 | $80$ | $2$ | $2$ | $5$ |
| 80.192.5-80.gc.2.4 | $80$ | $2$ | $2$ | $5$ |
| 80.192.5-80.go.2.4 | $80$ | $2$ | $2$ | $5$ |
| 80.192.5-80.gq.1.4 | $80$ | $2$ | $2$ | $5$ |
| 80.192.5-80.hb.2.5 | $80$ | $2$ | $2$ | $5$ |
| 80.192.5-80.hc.2.1 | $80$ | $2$ | $2$ | $5$ |
| 80.480.19-80.cn.1.8 | $80$ | $5$ | $5$ | $19$ |
| 240.192.5-240.qv.2.6 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.qx.2.8 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.sb.2.6 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.sf.2.8 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.sz.1.7 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.td.1.3 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.uj.1.7 | $240$ | $2$ | $2$ | $5$ |
| 240.192.5-240.ul.1.3 | $240$ | $2$ | $2$ | $5$ |
| 240.288.11-240.fo.2.14 | $240$ | $3$ | $3$ | $11$ |
| 240.384.13-240.dy.1.11 | $240$ | $4$ | $4$ | $13$ |