Invariants
| Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $6 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot8\cdot14^{2}\cdot56$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 6$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 56D6 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}1&0\\8&51\end{bmatrix}$, $\begin{bmatrix}23&220\\256&171\end{bmatrix}$, $\begin{bmatrix}36&13\\31&194\end{bmatrix}$, $\begin{bmatrix}70&237\\213&32\end{bmatrix}$, $\begin{bmatrix}85&104\\148&101\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.96.6.d.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $24$ |
| Cyclic 280-torsion field degree: | $2304$ |
| Full 280-torsion field degree: | $7741440$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 56.96.2-28.b.1.1 | $56$ | $2$ | $2$ | $2$ | $0$ |
| 280.96.2-28.b.1.15 | $280$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.384.11-280.bb.1.18 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.di.2.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.dt.1.6 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.dy.1.8 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.go.1.12 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.gr.2.14 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.gs.1.7 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.gv.1.8 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.jf.2.10 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.jh.2.9 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.jj.2.2 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.jl.2.6 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.kk.2.12 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.kn.2.10 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.ko.2.3 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.kr.2.6 | $280$ | $2$ | $2$ | $11$ |