Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20H3 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}81&60\\234&197\end{bmatrix}$, $\begin{bmatrix}109&210\\224&139\end{bmatrix}$, $\begin{bmatrix}111&210\\47&131\end{bmatrix}$, $\begin{bmatrix}217&160\\230&193\end{bmatrix}$, $\begin{bmatrix}227&180\\57&267\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.72.3.cx.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $32$ |
| Cyclic 280-torsion field degree: | $3072$ |
| Full 280-torsion field degree: | $10321920$ |
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
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.72.1-20.b.1.9 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 280.72.1-20.b.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.288.5-280.z.2.11 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.cu.2.7 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.gt.1.2 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.gw.1.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.my.1.3 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.na.1.8 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.nt.1.2 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.nu.1.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.pc.2.13 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.pd.2.3 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.px.1.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.py.1.2 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.rg.1.14 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.rh.1.3 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.sb.1.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.sc.1.2 | $280$ | $2$ | $2$ | $5$ |