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 | $2^{4}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot4$ | ||
| 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: | 8G0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}33&162\\138&19\end{bmatrix}$, $\begin{bmatrix}101&190\\68&7\end{bmatrix}$, $\begin{bmatrix}169&190\\54&267\end{bmatrix}$, $\begin{bmatrix}247&182\\170&141\end{bmatrix}$, $\begin{bmatrix}251&158\\218&277\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.24.0.v.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 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 |
|---|---|---|---|---|---|
| 40.24.0-4.a.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.24.0-4.a.1.1 | $56$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.96.1-280.a.1.4 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.c.1.3 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.f.1.5 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.g.1.6 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.i.1.5 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.k.1.7 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.n.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.t.1.3 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.bd.1.8 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.be.1.7 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.bh.1.1 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.bi.1.2 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.bl.1.1 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.bm.1.5 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.bp.1.8 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.bq.1.7 | $280$ | $2$ | $2$ | $1$ |
| 280.240.8-280.be.1.13 | $280$ | $5$ | $5$ | $8$ |
| 280.288.7-280.ca.1.3 | $280$ | $6$ | $6$ | $7$ |
| 280.384.11-280.cu.1.2 | $280$ | $8$ | $8$ | $11$ |
| 280.480.15-280.cq.1.25 | $280$ | $10$ | $10$ | $15$ |