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: | $10$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| 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: | 8N0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}31&240\\240&229\end{bmatrix}$, $\begin{bmatrix}71&40\\118&27\end{bmatrix}$, $\begin{bmatrix}79&132\\224&93\end{bmatrix}$, $\begin{bmatrix}119&40\\50&47\end{bmatrix}$, $\begin{bmatrix}135&88\\144&251\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.bf.2 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 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 |
|---|---|---|---|---|---|
| 40.48.0-8.e.1.9 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.48.0-8.e.1.16 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 140.48.0-140.c.1.7 | $140$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-140.c.1.30 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.u.1.26 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.u.1.63 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.cd.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.da.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ea.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.eg.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jd.1.13 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jf.1.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.js.1.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ju.1.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.me.1.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mg.1.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mv.1.13 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mx.1.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.oo.1.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ou.1.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pa.1.15 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pd.1.15 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.bt.2.18 | $280$ | $5$ | $5$ | $16$ |