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 | $1^{2}\cdot2^{2}$ | ||
| 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: | $\begin{bmatrix}33&46\\112&141\end{bmatrix}$, $\begin{bmatrix}175&149\\208&49\end{bmatrix}$, $\begin{bmatrix}239&87\\204&231\end{bmatrix}$, $\begin{bmatrix}251&77\\116&19\end{bmatrix}$, $\begin{bmatrix}267&11\\232&273\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.120.8.dt.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $48$ |
| Cyclic 280-torsion field degree: | $2304$ |
| 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 |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
| 56.48.0-56.bh.1.5 | $56$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.4-40.bl.1.7 | $40$ | $2$ | $2$ | $4$ | $0$ |
| 56.48.0-56.bh.1.5 | $56$ | $5$ | $5$ | $0$ | $0$ |
| 280.120.4-280.be.1.2 | $280$ | $2$ | $2$ | $4$ | $?$ |
| 280.120.4-280.be.1.14 | $280$ | $2$ | $2$ | $4$ | $?$ |
| 280.120.4-40.bl.1.16 | $280$ | $2$ | $2$ | $4$ | $?$ |
| 280.120.4-280.cd.1.12 | $280$ | $2$ | $2$ | $4$ | $?$ |
| 280.120.4-280.cd.1.18 | $280$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.480.16-280.ey.1.7 | $280$ | $2$ | $2$ | $16$ |
| 280.480.16-280.ey.2.8 | $280$ | $2$ | $2$ | $16$ |
| 280.480.16-280.ez.1.4 | $280$ | $2$ | $2$ | $16$ |
| 280.480.16-280.ez.2.15 | $280$ | $2$ | $2$ | $16$ |
| 280.480.16-280.fa.1.7 | $280$ | $2$ | $2$ | $16$ |
| 280.480.16-280.fa.2.8 | $280$ | $2$ | $2$ | $16$ |
| 280.480.16-280.fb.1.4 | $280$ | $2$ | $2$ | $16$ |
| 280.480.16-280.fb.2.15 | $280$ | $2$ | $2$ | $16$ |