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: | $\begin{bmatrix}41&28\\76&225\end{bmatrix}$, $\begin{bmatrix}43&276\\272&71\end{bmatrix}$, $\begin{bmatrix}51&148\\108&25\end{bmatrix}$, $\begin{bmatrix}65&218\\168&229\end{bmatrix}$, $\begin{bmatrix}231&118\\12&109\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.bd.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.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.48.0-8.e.1.12 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-140.c.1.22 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-140.c.1.31 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.24 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.52 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.be.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.da.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.dy.1.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.eg.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.iz.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jh.1.12 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jo.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.jw.2.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ma.1.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mi.2.8 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mr.2.16 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.mz.1.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.om.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ou.2.7 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.oz.2.15 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pd.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.br.2.20 | $280$ | $5$ | $5$ | $16$ |