Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}1&128\\258&43\end{bmatrix}$, $\begin{bmatrix}41&160\\168&117\end{bmatrix}$, $\begin{bmatrix}113&32\\84&167\end{bmatrix}$, $\begin{bmatrix}137&120\\120&133\end{bmatrix}$, $\begin{bmatrix}149&192\\224&109\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.0.cz.2 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $48$ |
Cyclic 280-torsion field degree: | $4608$ |
Full 280-torsion field degree: | $15482880$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-8.i.1.12 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.2.2 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.2.32 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.ej.1.10 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.ej.1.23 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
280.192.1-280.bu.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.fp.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ky.2.3 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.lc.2.3 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.oa.2.3 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.oe.2.3 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.pa.2.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.pi.2.5 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.ea.2.1 | $280$ | $5$ | $5$ | $16$ |