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: | $12$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot7^{2}\cdot8^{2}\cdot14\cdot28\cdot56^{2}$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 11$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 11$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 56P11 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}61&162\\56&223\end{bmatrix}$, $\begin{bmatrix}102&151\\145&108\end{bmatrix}$, $\begin{bmatrix}131&188\\98&277\end{bmatrix}$, $\begin{bmatrix}144&177\\91&230\end{bmatrix}$, $\begin{bmatrix}199&190\\140&249\end{bmatrix}$, $\begin{bmatrix}277&198\\218&33\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.192.11.mz.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $6$ |
| Cyclic 280-torsion field degree: | $576$ |
| Full 280-torsion field degree: | $3870720$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| 56.192.5-56.bl.1.24 | $56$ | $2$ | $2$ | $5$ | $0$ |
| 280.48.0-280.ej.1.11 | $280$ | $8$ | $8$ | $0$ | $?$ |
| 280.192.5-56.bl.1.9 | $280$ | $2$ | $2$ | $5$ | $?$ |