Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{2}\cdot40^{4}$ | Cusp orbits | $2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 30$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 16$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40B16 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}3&74\\88&57\end{bmatrix}$, $\begin{bmatrix}3&206\\228&117\end{bmatrix}$, $\begin{bmatrix}81&224\\88&225\end{bmatrix}$, $\begin{bmatrix}139&48\\36&3\end{bmatrix}$, $\begin{bmatrix}279&112\\196&221\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.240.16.dh.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $3096576$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $96$ | $48$ | $0$ | $0$ |
| 56.96.0-56.v.1.13 | $56$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.240.8-40.n.2.9 | $40$ | $2$ | $2$ | $8$ | $0$ |
| 56.96.0-56.v.1.13 | $56$ | $5$ | $5$ | $0$ | $0$ |
| 280.240.8-40.n.2.27 | $280$ | $2$ | $2$ | $8$ | $?$ |
| 280.240.8-280.bd.2.46 | $280$ | $2$ | $2$ | $8$ | $?$ |
| 280.240.8-280.bd.2.48 | $280$ | $2$ | $2$ | $8$ | $?$ |
| 280.240.8-280.bl.1.21 | $280$ | $2$ | $2$ | $8$ | $?$ |
| 280.240.8-280.bl.1.24 | $280$ | $2$ | $2$ | $8$ | $?$ |