Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $5^{4}\cdot10^{2}\cdot40^{2}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40G7 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}12&143\\245&18\end{bmatrix}$, $\begin{bmatrix}153&174\\126&257\end{bmatrix}$, $\begin{bmatrix}172&261\\23&178\end{bmatrix}$, $\begin{bmatrix}180&97\\167&250\end{bmatrix}$, $\begin{bmatrix}201&264\\210&99\end{bmatrix}$, $\begin{bmatrix}271&26\\182&19\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.120.7.cv.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $6193152$ |
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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(5)$ | $5$ | $24$ | $12$ | $0$ | $0$ |
| 56.24.0-56.z.1.8 | $56$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.3-20.c.1.10 | $40$ | $2$ | $2$ | $3$ | $0$ |
| 56.24.0-56.z.1.8 | $56$ | $10$ | $10$ | $0$ | $0$ |
| 280.120.3-20.c.1.5 | $280$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.