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: | $\begin{bmatrix}107&34\\140&3\end{bmatrix}$, $\begin{bmatrix}171&191\\176&279\end{bmatrix}$, $\begin{bmatrix}177&274\\24&175\end{bmatrix}$, $\begin{bmatrix}265&21\\84&135\end{bmatrix}$, $\begin{bmatrix}273&177\\204&207\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.240.15.fw.1 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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
| 56.48.0-56.v.1.2 | $56$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.240.7-40.bu.1.11 | $40$ | $2$ | $2$ | $7$ | $4$ |
| 56.48.0-56.v.1.2 | $56$ | $10$ | $10$ | $0$ | $0$ |
| 280.240.7-40.bu.1.4 | $280$ | $2$ | $2$ | $7$ | $?$ |
| 280.240.7-280.cu.1.5 | $280$ | $2$ | $2$ | $7$ | $?$ |
| 280.240.7-280.cu.1.56 | $280$ | $2$ | $2$ | $7$ | $?$ |
| 280.240.7-280.cv.1.1 | $280$ | $2$ | $2$ | $7$ | $?$ |
| 280.240.7-280.cv.1.52 | $280$ | $2$ | $2$ | $7$ | $?$ |