Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | 8C0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}9&124\\70&67\end{bmatrix}$, $\begin{bmatrix}10&9\\21&6\end{bmatrix}$, $\begin{bmatrix}42&167\\173&52\end{bmatrix}$, $\begin{bmatrix}57&224\\182&167\end{bmatrix}$, $\begin{bmatrix}111&172\\160&171\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.12.0.z.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $61931520$ |
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 |
|---|---|---|---|---|---|
| 40.12.0-4.c.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.12.0-4.c.1.2 | $56$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.48.0-280.y.1.19 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ba.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.bi.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.bj.1.10 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ca.1.11 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.cd.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.cf.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.cg.1.10 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.cr.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.cs.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.cu.1.10 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.cx.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.dh.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.di.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.dw.1.10 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.dz.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.120.4-280.bz.1.25 | $280$ | $5$ | $5$ | $4$ |
| 280.144.3-280.cl.1.9 | $280$ | $6$ | $6$ | $3$ |
| 280.192.5-280.bz.1.25 | $280$ | $8$ | $8$ | $5$ |
| 280.240.7-280.cx.1.7 | $280$ | $10$ | $10$ | $7$ |
| 280.504.16-280.cx.1.52 | $280$ | $21$ | $21$ | $16$ |