Invariants
| Level: | $80$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $9 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $10^{2}\cdot20\cdot80$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 80A9 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}13&52\\54&27\end{bmatrix}$, $\begin{bmatrix}48&39\\77&22\end{bmatrix}$, $\begin{bmatrix}74&63\\17&76\end{bmatrix}$, $\begin{bmatrix}75&12\\36&11\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.120.9.h.1 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $24$ |
| Cyclic 80-torsion field degree: | $768$ |
| Full 80-torsion field degree: | $49152$ |
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 |
|---|---|---|---|---|---|
| 40.120.4-40.bq.1.2 | $40$ | $2$ | $2$ | $4$ | $1$ |
| 80.48.1-80.d.1.14 | $80$ | $5$ | $5$ | $1$ | $?$ |
| 80.120.4-40.bq.1.6 | $80$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 80.480.17-80.c.2.17 | $80$ | $2$ | $2$ | $17$ |
| 80.480.17-80.i.1.5 | $80$ | $2$ | $2$ | $17$ |
| 80.480.17-80.ba.1.5 | $80$ | $2$ | $2$ | $17$ |
| 80.480.17-80.be.1.1 | $80$ | $2$ | $2$ | $17$ |
| 80.480.17-80.du.1.10 | $80$ | $2$ | $2$ | $17$ |
| 80.480.17-80.dx.1.6 | $80$ | $2$ | $2$ | $17$ |
| 80.480.17-80.dy.1.4 | $80$ | $2$ | $2$ | $17$ |
| 80.480.17-80.eb.1.2 | $80$ | $2$ | $2$ | $17$ |
| 240.480.17-240.dn.1.7 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.dp.1.5 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.dr.1.5 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.dt.1.5 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kp.1.11 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kr.1.10 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kt.1.11 | $240$ | $2$ | $2$ | $17$ |
| 240.480.17-240.kv.1.10 | $240$ | $2$ | $2$ | $17$ |