Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $120$ | $\PSL_2$-index: | $60$ | ||||
| Genus: | $4 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $10^{2}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A4 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}41&221\\232&161\end{bmatrix}$, $\begin{bmatrix}51&219\\268&113\end{bmatrix}$, $\begin{bmatrix}129&23\\40&157\end{bmatrix}$, $\begin{bmatrix}209&15\\248&83\end{bmatrix}$, $\begin{bmatrix}223&218\\112&5\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.60.4.k.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $12386304$ |
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 |
|---|---|---|---|---|---|
| 40.60.2-20.c.1.6 | $40$ | $2$ | $2$ | $2$ | $0$ |
| 280.24.0-28.g.1.6 | $280$ | $5$ | $5$ | $0$ | $?$ |
| 280.60.2-20.c.1.7 | $280$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.240.8-280.dq.1.5 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dq.1.14 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dr.1.11 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dr.1.20 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dy.1.1 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dy.1.11 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dz.1.5 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dz.1.9 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.eg.1.5 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.eg.1.9 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.eh.1.1 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.eh.1.10 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.ek.1.7 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.ek.1.13 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.el.1.5 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.el.1.15 | $280$ | $2$ | $2$ | $8$ |
| 280.360.10-140.s.1.9 | $280$ | $3$ | $3$ | $10$ |
| 280.480.13-140.eu.1.6 | $280$ | $4$ | $4$ | $13$ |