Invariants
| Level: | $280$ | $\SL_2$-level: | $56$ | 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: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot14^{2}\cdot28^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 28E5 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}73&70\\263&17\end{bmatrix}$, $\begin{bmatrix}127&42\\133&107\end{bmatrix}$, $\begin{bmatrix}195&154\\42&41\end{bmatrix}$, $\begin{bmatrix}223&14\\188&57\end{bmatrix}$, $\begin{bmatrix}223&168\\83&159\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.96.5.bk.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $24$ |
| Cyclic 280-torsion field degree: | $2304$ |
| Full 280-torsion field degree: | $7741440$ |
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 |
|---|---|---|---|---|---|
| 56.96.2-28.b.1.14 | $56$ | $2$ | $2$ | $2$ | $0$ |
| 280.24.0-280.m.1.6 | $280$ | $8$ | $8$ | $0$ | $?$ |
| 280.96.2-28.b.1.15 | $280$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.384.11-280.km.1.6 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.km.1.8 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.km.2.6 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.km.2.8 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.kn.1.10 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.kn.1.12 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.kn.2.10 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.kn.2.12 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mi.1.11 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mi.1.12 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mi.2.11 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mi.2.12 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mj.1.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mj.1.14 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mj.2.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mj.2.14 | $280$ | $2$ | $2$ | $11$ |