Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8I0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}1&158\\112&159\end{bmatrix}$, $\begin{bmatrix}51&106\\122&35\end{bmatrix}$, $\begin{bmatrix}58&137\\233&106\end{bmatrix}$, $\begin{bmatrix}116&259\\223&256\end{bmatrix}$, $\begin{bmatrix}240&147\\223&164\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.24.0.ej.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $48$ |
| Cyclic 280-torsion field degree: | $4608$ |
| Full 280-torsion field degree: | $30965760$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.n.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 280.24.0-8.n.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.96.0-280.cz.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.da.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.db.2.8 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.dd.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.df.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.dg.2.6 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.di.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.dl.2.7 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.dp.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.dq.2.6 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.ds.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.dv.2.14 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.dz.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.ea.2.5 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.ee.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.el.2.13 | $280$ | $2$ | $2$ | $0$ |
| 280.240.8-280.ge.2.5 | $280$ | $5$ | $5$ | $8$ |
| 280.288.7-280.kx.1.21 | $280$ | $6$ | $6$ | $7$ |
| 280.384.11-280.mz.2.9 | $280$ | $8$ | $8$ | $11$ |
| 280.480.15-280.og.2.9 | $280$ | $10$ | $10$ | $15$ |