Invariants
| Level: | $280$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{4}$ | Cusp orbits | $4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20C7 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}11&139\\274&259\end{bmatrix}$, $\begin{bmatrix}11&182\\132&215\end{bmatrix}$, $\begin{bmatrix}131&78\\34&199\end{bmatrix}$, $\begin{bmatrix}155&89\\194&143\end{bmatrix}$, $\begin{bmatrix}227&22\\222&191\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.120.7.bq.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $18432$ |
| Full 280-torsion field degree: | $6193152$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 20.120.3-20.a.1.5 | $20$ | $2$ | $2$ | $3$ | $0$ |
| 280.24.0-280.j.1.4 | $280$ | $10$ | $10$ | $0$ | $?$ |
| 280.120.3-20.a.1.2 | $280$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.480.13-280.rg.1.8 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.rh.1.5 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.rn.1.1 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.ro.1.7 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.ru.1.8 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.rv.1.3 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.sb.1.7 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.sc.1.8 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.wq.1.5 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.ws.1.7 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.wx.1.4 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.wz.1.3 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.xe.1.6 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.xg.1.2 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.xl.1.5 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.xn.1.5 | $280$ | $2$ | $2$ | $13$ |