Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{8}\cdot40^{4}$ | Cusp orbits | $2^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 28$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 15$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40C15 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}83&2\\252&167\end{bmatrix}$, $\begin{bmatrix}97&104\\194&255\end{bmatrix}$, $\begin{bmatrix}127&66\\28&223\end{bmatrix}$, $\begin{bmatrix}131&70\\100&211\end{bmatrix}$, $\begin{bmatrix}153&48\\38&39\end{bmatrix}$, $\begin{bmatrix}193&120\\270&223\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.240.15.cu.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $3096576$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
| 56.48.0-56.j.1.7 | $56$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 20.240.7-20.a.1.8 | $20$ | $2$ | $2$ | $7$ | $2$ |
| 56.48.0-56.j.1.7 | $56$ | $10$ | $10$ | $0$ | $0$ |
| 280.240.7-20.a.1.19 | $280$ | $2$ | $2$ | $7$ | $?$ |