Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $8^{4}\cdot16^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16C5 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}5&2\\14&21\end{bmatrix}$, $\begin{bmatrix}27&72\\4&71\end{bmatrix}$, $\begin{bmatrix}45&22\\52&15\end{bmatrix}$, $\begin{bmatrix}45&66\\46&69\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.96.5.bj.2 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 |
|---|---|---|---|---|---|
| 8.96.1-8.i.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 80.96.1-8.i.2.2 | $80$ | $2$ | $2$ | $1$ | $?$ |
| 80.96.3-80.c.1.15 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.96.3-80.c.1.17 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.96.3-80.d.1.4 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.96.3-80.d.1.15 | $80$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 80.384.9-80.fy.1.12 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.gf.2.1 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.gs.1.3 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.gv.2.1 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.it.1.1 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.iw.1.15 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.jo.3.3 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.jx.1.9 | $80$ | $2$ | $2$ | $9$ |
| 240.384.9-240.st.1.13 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.tj.2.4 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.xf.2.2 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.xs.1.15 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bcy.1.13 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bdl.2.5 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bhm.2.7 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bic.1.9 | $240$ | $2$ | $2$ | $9$ |