Invariants
| Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
| Index: | $504$ | $\PSL_2$-index: | $252$ | ||||
| Genus: | $13 = 1 + \frac{ 252 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (none of which are rational) | Cusp widths | $7^{12}\cdot28^{6}$ | Cusp orbits | $6\cdot12$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 13$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 28C13 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}25&14\\138&213\end{bmatrix}$, $\begin{bmatrix}27&22\\82&169\end{bmatrix}$, $\begin{bmatrix}60&139\\1&218\end{bmatrix}$, $\begin{bmatrix}154&271\\149&92\end{bmatrix}$, $\begin{bmatrix}191&154\\230&47\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.252.13.h.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $18432$ |
| Full 280-torsion field degree: | $2949120$ |
Rational points
This modular curve has no $\Q_p$ points for $p=17,37$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 56.252.7-28.b.1.9 | $56$ | $2$ | $2$ | $7$ | $0$ |
| 280.252.7-28.b.1.6 | $280$ | $2$ | $2$ | $7$ | $?$ |