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 | $3^{2}\cdot6$ | ||
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: | 28C16 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}77&265\\184&259\end{bmatrix}$, $\begin{bmatrix}117&24\\168&149\end{bmatrix}$, $\begin{bmatrix}157&158\\176&47\end{bmatrix}$, $\begin{bmatrix}159&269\\56&149\end{bmatrix}$, $\begin{bmatrix}163&231\\252&275\end{bmatrix}$, $\begin{bmatrix}231&177\\52&77\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.252.16.s.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $2949120$ |
Rational points
This modular curve has no $\Q_p$ points for $p=11$, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(7)$ | $7$ | $24$ | $12$ | $0$ | $0$ |
40.24.0-20.g.1.3 | $40$ | $21$ | $21$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.24.0-20.g.1.3 | $40$ | $21$ | $21$ | $0$ | $0$ |
56.252.7-28.c.1.19 | $56$ | $2$ | $2$ | $7$ | $0$ |
280.252.7-28.c.1.11 | $280$ | $2$ | $2$ | $7$ | $?$ |