Invariants
Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
Index: | $504$ | $\PSL_2$-index: | $252$ | ||||
Genus: | $16 = 1 + \frac{ 252 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $14^{6}\cdot28^{6}$ | Cusp orbits | $6^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $5 \le \gamma \le 30$ | ||||||
$\overline{\Q}$-gonality: | $5 \le \gamma \le 16$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 28A16 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}87&26\\44&235\end{bmatrix}$, $\begin{bmatrix}109&37\\68&101\end{bmatrix}$, $\begin{bmatrix}109&196\\126&67\end{bmatrix}$, $\begin{bmatrix}135&37\\46&87\end{bmatrix}$, $\begin{bmatrix}181&89\\98&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.252.16.dz.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 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 |
---|---|---|---|---|---|
56.252.7-28.b.1.15 | $56$ | $2$ | $2$ | $7$ | $0$ |
280.252.7-28.b.1.6 | $280$ | $2$ | $2$ | $7$ | $?$ |