Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $8^{24}$ | Cusp orbits | $2^{2}\cdot4^{3}\cdot8$ | ||
| 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: | 8A5 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}3&42\\16&153\end{bmatrix}$, $\begin{bmatrix}91&136\\96&219\end{bmatrix}$, $\begin{bmatrix}217&30\\184&31\end{bmatrix}$, $\begin{bmatrix}257&108\\160&273\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.192.5.bh.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $48$ |
| Cyclic 280-torsion field degree: | $2304$ |
| Full 280-torsion field degree: | $3870720$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=17$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.192.1-40.f.1.5 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 56.192.3-56.p.2.7 | $56$ | $2$ | $2$ | $3$ | $0$ |
| 280.192.1-40.f.1.12 | $280$ | $2$ | $2$ | $1$ | $?$ |
| 280.192.1-280.h.1.1 | $280$ | $2$ | $2$ | $1$ | $?$ |
| 280.192.1-280.h.1.21 | $280$ | $2$ | $2$ | $1$ | $?$ |
| 280.192.1-280.bp.1.13 | $280$ | $2$ | $2$ | $1$ | $?$ |
| 280.192.1-280.bp.1.21 | $280$ | $2$ | $2$ | $1$ | $?$ |
| 280.192.3-56.p.2.6 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.192.3-280.r.1.1 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.192.3-280.r.1.14 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.192.3-280.bs.3.2 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.192.3-280.bs.3.13 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.192.3-280.cb.2.1 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.192.3-280.cb.2.6 | $280$ | $2$ | $2$ | $3$ | $?$ |