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: | $\begin{bmatrix}53&72\\22&91\end{bmatrix}$, $\begin{bmatrix}121&204\\226&181\end{bmatrix}$, $\begin{bmatrix}163&148\\46&97\end{bmatrix}$, $\begin{bmatrix}207&248\\182&81\end{bmatrix}$, $\begin{bmatrix}261&60\\150&159\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.0.cw.1 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 |
---|---|---|---|---|---|
40.48.0-8.h.1.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
56.48.0-8.h.1.7 | $56$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-280.u.1.38 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.1.42 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.2.41 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.2.60 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.bt.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.bt.2.11 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ch.1.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ch.2.9 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ks.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ks.2.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kt.1.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kt.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.nu.1.3 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.nu.2.13 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.nv.1.7 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.nv.2.9 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.oo.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.oo.2.11 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.op.1.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.op.2.3 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.du.1.22 | $280$ | $5$ | $5$ | $16$ |