Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot10^{4}\cdot40^{2}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40M7 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}71&120\\275&129\end{bmatrix}$, $\begin{bmatrix}117&260\\200&231\end{bmatrix}$, $\begin{bmatrix}143&140\\169&253\end{bmatrix}$, $\begin{bmatrix}169&220\\18&1\end{bmatrix}$, $\begin{bmatrix}211&20\\74&271\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.144.7.gq.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $16$ |
| Cyclic 280-torsion field degree: | $1536$ |
| Full 280-torsion field degree: | $5160960$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.144.3-20.p.1.2 | $40$ | $2$ | $2$ | $3$ | $1$ |
| 280.48.0-280.cj.1.15 | $280$ | $6$ | $6$ | $0$ | $?$ |
| 280.144.3-20.p.1.11 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.144.3-280.cr.1.30 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.144.3-280.cr.1.47 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.144.3-280.ct.1.22 | $280$ | $2$ | $2$ | $3$ | $?$ |
| 280.144.3-280.ct.1.39 | $280$ | $2$ | $2$ | $3$ | $?$ |