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: | $\begin{bmatrix}30&169\\259&152\end{bmatrix}$, $\begin{bmatrix}34&75\\219&148\end{bmatrix}$, $\begin{bmatrix}113&56\\56&239\end{bmatrix}$, $\begin{bmatrix}132&209\\211&206\end{bmatrix}$, $\begin{bmatrix}269&112\\100&277\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.252.13.bb.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 real points and no $\Q_p$ points for $p=17,29$, 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.1.4 | $56$ | $2$ | $2$ | $7$ | $0$ |
280.252.7-28.b.1.6 | $280$ | $2$ | $2$ | $7$ | $?$ |