Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $8^{12}$ | Cusp orbits | $2^{4}\cdot4$ | ||
| 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: | 8B3 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}67&178\\248&41\end{bmatrix}$, $\begin{bmatrix}89&112\\252&53\end{bmatrix}$, $\begin{bmatrix}97&4\\200&189\end{bmatrix}$, $\begin{bmatrix}99&24\\276&55\end{bmatrix}$, $\begin{bmatrix}217&142\\32&263\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.96.3.cb.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $4608$ |
| Full 280-torsion field degree: | $7741440$ |
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 |
|---|---|---|---|---|---|
| 40.96.0-40.b.2.10 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 280.96.0-40.b.2.19 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 56.96.2-56.a.1.2 | $56$ | $2$ | $2$ | $2$ | $0$ |
| 280.96.2-56.a.1.15 | $280$ | $2$ | $2$ | $2$ | $?$ |
| 280.96.1-280.o.2.11 | $280$ | $2$ | $2$ | $1$ | $?$ |
| 280.96.1-280.o.2.39 | $280$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.384.5-280.i.2.14 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.j.1.2 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.be.2.16 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.bh.2.1 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.ci.1.4 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.cj.2.13 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.do.1.2 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.dp.2.15 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.eu.2.15 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.ev.2.2 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.fs.1.13 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.ft.2.4 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.gk.2.1 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.gn.3.16 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.he.2.2 | $280$ | $2$ | $2$ | $5$ |
| 280.384.5-280.hf.2.14 | $280$ | $2$ | $2$ | $5$ |