Invariants
| Level: | $280$ | $\SL_2$-level: | $4$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
| 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: | 4G0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}47&216\\102&15\end{bmatrix}$, $\begin{bmatrix}77&6\\90&189\end{bmatrix}$, $\begin{bmatrix}271&170\\132&103\end{bmatrix}$, $\begin{bmatrix}273&80\\202&259\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.24.0.i.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $18432$ |
| Full 280-torsion field degree: | $30965760$ |
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 |
|---|---|---|---|---|---|
| 28.24.0-28.a.1.4 | $28$ | $2$ | $2$ | $0$ | $0$ |
| 40.24.0-40.a.1.7 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 280.24.0-28.a.1.1 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.24.0-40.a.1.1 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.24.0-280.a.1.7 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.24.0-280.a.1.16 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.240.8-280.p.1.12 | $280$ | $5$ | $5$ | $8$ |
| 280.288.7-280.r.1.5 | $280$ | $6$ | $6$ | $7$ |
| 280.384.11-280.p.1.18 | $280$ | $8$ | $8$ | $11$ |
| 280.480.15-280.p.1.21 | $280$ | $10$ | $10$ | $15$ |