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: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-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: | $\begin{bmatrix}7&190\\80&199\end{bmatrix}$, $\begin{bmatrix}85&24\\252&55\end{bmatrix}$, $\begin{bmatrix}115&14\\132&163\end{bmatrix}$, $\begin{bmatrix}171&120\\176&239\end{bmatrix}$, $\begin{bmatrix}247&22\\268&205\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.0.j.2 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $15482880$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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.c.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ |
56.48.0-56.h.1.28 | $56$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-20.c.1.15 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.h.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.1.11 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.1.53 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.q.2.7 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.cb.1.7 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.dc.1.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.dg.2.7 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.fq.2.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.gc.1.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.gg.1.1 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.gs.2.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ic.1.1 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.io.2.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.is.2.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.je.1.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ko.1.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ks.2.7 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kw.2.7 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ky.1.7 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.p.1.17 | $280$ | $5$ | $5$ | $16$ |