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 $4$ are rational) | Cusp widths | $8^{4}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| 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: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16C5 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}1&18\\40&63\end{bmatrix}$, $\begin{bmatrix}3&54\\44&49\end{bmatrix}$, $\begin{bmatrix}29&44\\62&43\end{bmatrix}$, $\begin{bmatrix}47&24\\46&73\end{bmatrix}$, $\begin{bmatrix}49&0\\72&41\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.96.5.cj.2 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $24$ |
| Cyclic 80-torsion field degree: | $768$ |
| 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 |
|---|---|---|---|---|---|
| 16.96.1-8.k.2.5 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 40.96.1-8.k.2.4 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 80.96.3-80.d.1.16 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.96.3-80.d.1.18 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.96.3-80.f.2.11 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 80.96.3-80.f.2.19 | $80$ | $2$ | $2$ | $3$ | $?$ |
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.ct.2.11 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.cv.2.10 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.er.2.12 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.ex.2.12 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.jo.3.18 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.jq.2.9 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.kb.1.11 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.kc.2.5 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.ko.2.10 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.ku.2.10 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.ls.2.11 | $80$ | $2$ | $2$ | $9$ |
| 80.384.9-80.lu.2.10 | $80$ | $2$ | $2$ | $9$ |
| 240.384.9-240.jr.2.31 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.jt.2.28 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.oj.2.16 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.op.2.16 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bjn.2.6 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bjq.2.7 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bkf.2.15 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bki.2.14 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bmu.1.16 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bna.1.16 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bpm.1.31 | $240$ | $2$ | $2$ | $9$ |
| 240.384.9-240.bpo.1.28 | $240$ | $2$ | $2$ | $9$ |