Invariants
| Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot14^{2}\cdot28^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 28E5 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}3&112\\40&57\end{bmatrix}$, $\begin{bmatrix}47&252\\22&169\end{bmatrix}$, $\begin{bmatrix}79&28\\251&65\end{bmatrix}$, $\begin{bmatrix}81&168\\7&59\end{bmatrix}$, $\begin{bmatrix}183&168\\152&85\end{bmatrix}$, $\begin{bmatrix}187&168\\3&11\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.96.5.k.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $12$ |
| Cyclic 280-torsion field degree: | $1152$ |
| Full 280-torsion field degree: | $7741440$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| $X_0(7)$ | $7$ | $24$ | $12$ | $0$ | $0$ |
| 40.24.0-20.g.1.3 | $40$ | $8$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.24.0-20.g.1.3 | $40$ | $8$ | $8$ | $0$ | $0$ |
| 56.96.2-28.c.1.22 | $56$ | $2$ | $2$ | $2$ | $0$ |
| 280.96.2-28.c.1.26 | $280$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.