Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $8^{6}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8A2 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}61&34\\156&223\end{bmatrix}$, $\begin{bmatrix}77&134\\158&107\end{bmatrix}$, $\begin{bmatrix}143&148\\226&235\end{bmatrix}$, $\begin{bmatrix}163&2\\96&241\end{bmatrix}$, $\begin{bmatrix}191&192\\82&247\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.2.b.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $18432$ |
| Full 280-torsion field degree: | $15482880$ |
Rational points
This modular curve has no $\Q_p$ points for $p=3$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.48.0-20.b.1.9 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-20.b.1.3 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.192.3-280.h.1.3 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.j.1.3 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.l.1.1 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.n.1.1 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.cy.1.5 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.de.1.3 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.dg.1.1 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.dm.1.1 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.do.1.2 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.du.1.2 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.dw.1.6 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.ec.1.6 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.ee.1.2 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.eg.1.2 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.ei.1.4 | $280$ | $2$ | $2$ | $3$ |
| 280.192.3-280.ek.1.6 | $280$ | $2$ | $2$ | $3$ |
| 280.480.18-280.c.1.19 | $280$ | $5$ | $5$ | $18$ |