Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8O0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}21&276\\188&145\end{bmatrix}$, $\begin{bmatrix}69&24\\162&199\end{bmatrix}$, $\begin{bmatrix}159&20\\222&187\end{bmatrix}$, $\begin{bmatrix}267&188\\256&235\end{bmatrix}$, $\begin{bmatrix}275&108\\102&101\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.cs.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $15482880$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
|---|---|---|---|---|---|
| 40.48.0-40.m.1.14 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-40.m.1.1 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 56.48.0-56.i.1.6 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-56.i.1.2 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.1.23 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.1.29 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.192.1-280.x.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.bc.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cj.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cm.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fi.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fj.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fm.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fn.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mm.1.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mn.1.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.my.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mz.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.nc.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.nd.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.no.1.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.np.1.11 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.do.1.29 | $280$ | $5$ | $5$ | $16$ |