Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{3}\cdot8\cdot10^{2}\cdot20^{3}\cdot40$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40X7 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}7&60\\150&207\end{bmatrix}$, $\begin{bmatrix}9&160\\186&217\end{bmatrix}$, $\begin{bmatrix}81&240\\66&167\end{bmatrix}$, $\begin{bmatrix}83&180\\178&159\end{bmatrix}$, $\begin{bmatrix}109&0\\44&79\end{bmatrix}$, $\begin{bmatrix}139&80\\230&109\end{bmatrix}$, $\begin{bmatrix}181&180\\154&123\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.144.7.bl.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $16$ |
| Cyclic 280-torsion field degree: | $1536$ |
| Full 280-torsion field degree: | $5160960$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal 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 |
|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
| 56.48.0-56.i.1.6 | $56$ | $6$ | $6$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.144.3-20.b.1.28 | $40$ | $2$ | $2$ | $3$ | $0$ |
| 56.48.0-56.i.1.6 | $56$ | $6$ | $6$ | $0$ | $0$ |
| 280.144.3-20.b.1.20 | $280$ | $2$ | $2$ | $3$ | $?$ |