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 | $2^{5}$ | ||
| 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: | $\begin{bmatrix}17&48\\120&109\end{bmatrix}$, $\begin{bmatrix}33&200\\86&263\end{bmatrix}$, $\begin{bmatrix}39&216\\6&97\end{bmatrix}$, $\begin{bmatrix}65&104\\114&141\end{bmatrix}$, $\begin{bmatrix}249&156\\164&43\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.cb.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 |
|---|---|---|---|---|---|
| 40.48.0-8.e.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.48.0-8.e.1.14 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-280.t.2.46 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.52 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.y.1.36 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.y.1.37 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.bb.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.be.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cz.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.da.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.eo.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ep.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ew.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ex.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fw.2.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fx.2.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ge.1.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.gf.1.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.hs.1.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ht.1.13 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ia.2.2 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ib.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.cp.2.14 | $280$ | $5$ | $5$ | $16$ |