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 | $4^{8}\cdot8^{2}$ | 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: | 8N0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}101&106\\164&237\end{bmatrix}$, $\begin{bmatrix}121&252\\76&123\end{bmatrix}$, $\begin{bmatrix}139&142\\184&189\end{bmatrix}$, $\begin{bmatrix}265&6\\244&217\end{bmatrix}$, $\begin{bmatrix}271&160\\240&129\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.bk.1 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.1.11 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-40.i.1.29 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 56.48.0-56.h.1.13 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-56.h.1.23 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.e.1.9 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.e.1.31 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.s.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cw.2.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.em.2.5 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.eu.2.13 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ih.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ip.2.1 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.kc.2.1 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.kk.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.lj.2.5 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.lr.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ne.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.nm.2.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ol.2.7 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ot.2.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pg.2.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pk.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.by.1.3 | $280$ | $5$ | $5$ | $16$ |