Invariants
Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{8}\cdot40^{4}$ | Cusp orbits | $4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $6 \le \gamma \le 28$ | ||||||
$\overline{\Q}$-gonality: | $6 \le \gamma \le 15$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40C15 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}1&242\\0&9\end{bmatrix}$, $\begin{bmatrix}7&195\\184&83\end{bmatrix}$, $\begin{bmatrix}53&270\\16&217\end{bmatrix}$, $\begin{bmatrix}99&167\\276&161\end{bmatrix}$, $\begin{bmatrix}169&238\\28&135\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.240.15.lm.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $4608$ |
Full 280-torsion field degree: | $3096576$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=3$, 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 |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
56.48.0-56.bs.1.6 | $56$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.240.7-40.cw.1.24 | $40$ | $2$ | $2$ | $7$ | $2$ |
56.48.0-56.bs.1.6 | $56$ | $10$ | $10$ | $0$ | $0$ |
280.240.7-280.cf.1.3 | $280$ | $2$ | $2$ | $7$ | $?$ |
280.240.7-280.cf.1.20 | $280$ | $2$ | $2$ | $7$ | $?$ |
280.240.7-40.cw.1.1 | $280$ | $2$ | $2$ | $7$ | $?$ |
280.240.7-280.dj.1.21 | $280$ | $2$ | $2$ | $7$ | $?$ |
280.240.7-280.dj.1.56 | $280$ | $2$ | $2$ | $7$ | $?$ |