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 | $2^{3}\cdot4$ | ||
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: | $\begin{bmatrix}39&164\\186&187\end{bmatrix}$, $\begin{bmatrix}59&244\\244&101\end{bmatrix}$, $\begin{bmatrix}65&28\\256&201\end{bmatrix}$, $\begin{bmatrix}131&64\\178&53\end{bmatrix}$, $\begin{bmatrix}225&256\\166&119\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.0.cp.2 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
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 |
---|---|---|---|---|---|
40.48.0-40.l.1.14 | $40$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-40.l.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ |
56.48.0-56.i.1.6 | $56$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-56.i.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.1.20 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.1.31 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.bv.1.16 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.cg.1.12 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ci.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.cp.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.dg.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.dh.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.di.1.16 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.dj.1.12 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.lm.1.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ln.1.11 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.lo.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.lp.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.mc.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.md.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.me.1.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.mf.1.11 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.dl.1.17 | $280$ | $5$ | $5$ | $16$ |