Invariants
| Level: | $80$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16G1 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}40&37\\73&68\end{bmatrix}$, $\begin{bmatrix}48&69\\9&68\end{bmatrix}$, $\begin{bmatrix}60&27\\21&38\end{bmatrix}$, $\begin{bmatrix}74&25\\59&44\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.48.1.bu.2 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $12$ |
| Cyclic 80-torsion field degree: | $192$ |
| Full 80-torsion field degree: | $122880$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.48.0-8.ba.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 80.48.0-8.ba.1.3 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 80.48.0-80.n.1.23 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 80.48.0-80.n.1.29 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 80.48.1-80.a.1.9 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.48.1-80.a.1.32 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 80.192.1-80.d.1.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.w.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.bm.2.7 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.bt.1.4 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.ds.2.1 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.du.1.2 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.eg.2.3 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.192.1-80.em.1.4 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 80.480.17-80.cw.2.11 | $80$ | $5$ | $5$ | $17$ | $?$ | not computed |
| 240.192.1-240.ln.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.md.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.mt.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.nj.2.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.zb.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.zp.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.baf.2.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.bax.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.288.9-240.yc.2.38 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 240.384.9-240.ftj.2.52 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |