Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $9 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $20^{2}\cdot40^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A9 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}69&188\\258&75\end{bmatrix}$, $\begin{bmatrix}71&248\\120&219\end{bmatrix}$, $\begin{bmatrix}107&124\\188&179\end{bmatrix}$, $\begin{bmatrix}177&94\\242&243\end{bmatrix}$, $\begin{bmatrix}241&154\\98&211\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.120.9.b.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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
| 56.48.1-56.b.1.6 | $56$ | $5$ | $5$ | $1$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.4-20.a.1.6 | $40$ | $2$ | $2$ | $4$ | $1$ |
| 56.48.1-56.b.1.6 | $56$ | $5$ | $5$ | $1$ | $1$ |
| 140.120.4-20.a.1.3 | $140$ | $2$ | $2$ | $4$ | $?$ |
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.a.1.3 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.h.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.ba.2.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cb.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cf.1.5 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.ch.1.7 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.cr.1.11 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.ct.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gb.1.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gd.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gf.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gh.1.7 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gu.1.1 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gx.1.8 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gz.1.1 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.hb.1.8 | $280$ | $2$ | $2$ | $17$ |