Invariants
| Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $4 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot7^{4}\cdot8\cdot56$ | Cusp orbits | $1^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 56C4 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}12&189\\127&270\end{bmatrix}$, $\begin{bmatrix}47&224\\64&221\end{bmatrix}$, $\begin{bmatrix}49&30\\222&137\end{bmatrix}$, $\begin{bmatrix}82&125\\57&24\end{bmatrix}$, $\begin{bmatrix}251&96\\208&125\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.96.4.d.2 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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 7.16.0-7.a.1.1 | $7$ | $12$ | $12$ | $0$ | $0$ |
| 40.12.0-4.b.1.3 | $40$ | $16$ | $16$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 28.96.2-28.b.1.1 | $28$ | $2$ | $2$ | $2$ | $0$ |
| 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.ba.2.21 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.di.1.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.ds.2.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.dy.2.15 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.io.2.15 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.ir.1.15 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.is.2.15 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.iv.2.16 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.je.2.9 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.jh.2.9 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.ji.2.9 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.jl.2.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mg.2.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mj.2.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mk.2.13 | $280$ | $2$ | $2$ | $11$ |
| 280.384.11-280.mn.2.15 | $280$ | $2$ | $2$ | $11$ |