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: | $\begin{bmatrix}109&48\\140&37\end{bmatrix}$, $\begin{bmatrix}119&256\\4&19\end{bmatrix}$, $\begin{bmatrix}183&208\\104&165\end{bmatrix}$, $\begin{bmatrix}223&228\\56&39\end{bmatrix}$, $\begin{bmatrix}225&276\\18&93\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.cg.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.i.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-40.i.1.9 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 56.48.0-56.l.1.7 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-56.l.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.5 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.17 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.y.2.5 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.bg.2.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cq.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cx.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.dm.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.dn.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.dq.2.13 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.dr.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ig.2.2 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ih.2.2 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.iq.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ir.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jm.2.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jn.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jw.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jx.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.cw.2.5 | $280$ | $5$ | $5$ | $16$ |