Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $8 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $10^{4}\cdot40^{2}$ | Cusp orbits | $1^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A8 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}67&14\\214&185\end{bmatrix}$, $\begin{bmatrix}107&254\\162&153\end{bmatrix}$, $\begin{bmatrix}173&166\\206&55\end{bmatrix}$, $\begin{bmatrix}263&206\\190&9\end{bmatrix}$, $\begin{bmatrix}273&222\\164&49\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.120.8.be.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $18432$ |
| Full 280-torsion field degree: | $6193152$ |
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 |
|---|---|---|---|---|---|
| 40.120.4-20.a.1.11 | $40$ | $2$ | $2$ | $4$ | $1$ |
| 140.120.4-20.a.1.3 | $140$ | $2$ | $2$ | $4$ | $?$ |
| 280.48.0-280.v.1.10 | $280$ | $5$ | $5$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.480.17-280.c.1.5 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.f.1.7 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.n.1.7 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.o.1.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.q.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.s.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.bc.2.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.bp.1.7 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cf.1.5 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cg.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cj.1.7 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.ck.1.1 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cn.1.7 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.co.1.1 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cr.1.11 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cs.1.7 | $280$ | $2$ | $2$ | $17$ |