Invariants
| Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $11 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot14^{4}\cdot56^{2}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 20$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 11$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 56M11 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}1&0\\153&11\end{bmatrix}$, $\begin{bmatrix}33&28\\262&83\end{bmatrix}$, $\begin{bmatrix}37&112\\83&269\end{bmatrix}$, $\begin{bmatrix}179&196\\173&115\end{bmatrix}$, $\begin{bmatrix}249&196\\162&51\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.192.11.ic.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $12$ |
| Cyclic 280-torsion field degree: | $1152$ |
| Full 280-torsion field degree: | $3870720$ |
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 |
|---|---|---|---|---|---|
| 56.192.5-56.bm.1.29 | $56$ | $2$ | $2$ | $5$ | $3$ |
| 280.48.0-280.ce.1.12 | $280$ | $8$ | $8$ | $0$ | $?$ |
| 280.192.5-140.l.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ |
| 280.192.5-140.l.1.24 | $280$ | $2$ | $2$ | $5$ | $?$ |
| 280.192.5-56.bm.1.12 | $280$ | $2$ | $2$ | $5$ | $?$ |
| 280.192.5-280.by.1.22 | $280$ | $2$ | $2$ | $5$ | $?$ |
| 280.192.5-280.by.1.27 | $280$ | $2$ | $2$ | $5$ | $?$ |