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: | $\begin{bmatrix}41&246\\28&267\end{bmatrix}$, $\begin{bmatrix}141&128\\172&209\end{bmatrix}$, $\begin{bmatrix}153&46\\244&181\end{bmatrix}$, $\begin{bmatrix}211&66\\172&209\end{bmatrix}$, $\begin{bmatrix}253&58\\208&257\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.be.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.1.19 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.48.0-56.i.1.6 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-140.c.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-140.c.1.25 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-40.i.1.7 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-56.i.1.28 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.cn.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cv.2.8 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ec.2.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ee.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jb.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jh.2.8 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jq.2.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jw.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mc.2.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mi.2.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mt.2.8 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mz.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.oq.2.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.os.2.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pb.2.8 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pc.2.12 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.bs.1.24 | $280$ | $5$ | $5$ | $16$ |