Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{4}\cdot40^{4}$ | Cusp orbits | $4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 17$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A17 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}51&184\\80&203\end{bmatrix}$, $\begin{bmatrix}107&183\\114&89\end{bmatrix}$, $\begin{bmatrix}191&118\\124&83\end{bmatrix}$, $\begin{bmatrix}267&204\\142&17\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $18432$ |
| Full 280-torsion field degree: | $6193152$ |
Rational points
This modular curve has no real points, and therefore no 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 |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $48$ | $48$ | $0$ | $0$ |
| 56.48.1.hl.1 | $56$ | $5$ | $5$ | $1$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.8.fr.1 | $40$ | $2$ | $2$ | $8$ | $2$ |
| 56.48.1.hl.1 | $56$ | $5$ | $5$ | $1$ | $1$ |
| 280.120.8.hk.1 | $280$ | $2$ | $2$ | $8$ | $?$ |
| 280.120.8.if.1 | $280$ | $2$ | $2$ | $8$ | $?$ |
| 280.120.8.tb.1 | $280$ | $2$ | $2$ | $8$ | $?$ |
| 280.120.9.hl.1 | $280$ | $2$ | $2$ | $9$ | $?$ |
| 280.120.9.iz.1 | $280$ | $2$ | $2$ | $9$ | $?$ |
| 280.120.9.of.1 | $280$ | $2$ | $2$ | $9$ | $?$ |