Invariants
| Level: | $280$ | $\SL_2$-level: | $70$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $7 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot10\cdot14\cdot70$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 70C7 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}59&188\\41&171\end{bmatrix}$, $\begin{bmatrix}69&84\\205&183\end{bmatrix}$, $\begin{bmatrix}178&53\\237&159\end{bmatrix}$, $\begin{bmatrix}262&9\\211&240\end{bmatrix}$, $\begin{bmatrix}264&263\\227&200\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.96.7.j.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 |
|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $32$ | $16$ | $0$ | $0$ |
| 56.32.0-56.d.1.2 | $56$ | $6$ | $6$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 35.96.3-35.a.1.2 | $35$ | $2$ | $2$ | $3$ | $0$ |
| 56.32.0-56.d.1.2 | $56$ | $6$ | $6$ | $0$ | $0$ |
| 280.96.3-35.a.1.19 | $280$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.384.13-280.mh.1.21 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.mh.2.25 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.mj.1.3 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.mj.2.5 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.mn.1.1 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.mn.2.1 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.mp.1.1 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.mp.2.1 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.rc.1.5 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.rc.2.9 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.rd.1.3 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.rd.2.5 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.ri.1.1 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.ri.2.1 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.rj.1.1 | $280$ | $2$ | $2$ | $13$ |
| 280.384.13-280.rj.2.1 | $280$ | $2$ | $2$ | $13$ |