Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $120$ | $\PSL_2$-index: | $60$ | ||||
| Genus: | $4 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $5^{2}\cdot10\cdot40$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | 40B4 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}114&259\\109&276\end{bmatrix}$, $\begin{bmatrix}152&219\\57&22\end{bmatrix}$, $\begin{bmatrix}176&147\\163&144\end{bmatrix}$, $\begin{bmatrix}199&6\\210&247\end{bmatrix}$, $\begin{bmatrix}274&131\\253&148\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.60.4.bx.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $12386304$ |
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 |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $24$ | $12$ | $0$ | $0$ |
| 56.24.0-56.z.1.8 | $56$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.60.2-20.c.1.9 | $40$ | $2$ | $2$ | $2$ | $0$ |
| 56.24.0-56.z.1.8 | $56$ | $5$ | $5$ | $0$ | $0$ |
| 280.60.2-20.c.1.4 | $280$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.240.8-280.bl.1.30 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.bp.1.12 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.cb.1.7 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.cc.1.12 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.db.1.16 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dd.1.16 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dj.1.16 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dl.1.12 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dv.1.10 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.dw.1.16 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.ek.1.10 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.en.1.12 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.ff.1.16 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.fg.1.12 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.fm.1.16 | $280$ | $2$ | $2$ | $8$ |
| 280.240.8-280.fp.1.16 | $280$ | $2$ | $2$ | $8$ |
| 280.360.10-280.cv.1.47 | $280$ | $3$ | $3$ | $10$ |
| 280.480.13-280.bob.1.32 | $280$ | $4$ | $4$ | $13$ |