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 | $4^{8}\cdot8^{2}$ | 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: | 8N0 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}119&76\\116&135\end{bmatrix}$, $\begin{bmatrix}137&84\\256&53\end{bmatrix}$, $\begin{bmatrix}203&164\\124&5\end{bmatrix}$, $\begin{bmatrix}219&198\\176&41\end{bmatrix}$, $\begin{bmatrix}249&198\\64&27\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.0.p.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
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 |
---|---|---|---|---|---|
40.48.0-40.e.1.2 | $40$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-40.e.1.18 | $280$ | $2$ | $2$ | $0$ | $?$ |
56.48.0-56.i.1.19 | $56$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-56.i.1.16 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.1.24 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.1.34 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.cg.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.cp.2.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.fk.2.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.fm.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.hf.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.hh.2.9 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.hv.2.9 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.hx.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jr.2.10 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jt.1.1 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kh.1.1 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kj.2.10 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kt.2.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kv.1.1 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.lc.1.1 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ld.2.6 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.v.1.21 | $280$ | $5$ | $5$ | $16$ |