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: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-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: | $\begin{bmatrix}1&212\\136&221\end{bmatrix}$, $\begin{bmatrix}93&156\\168&67\end{bmatrix}$, $\begin{bmatrix}243&240\\142&9\end{bmatrix}$, $\begin{bmatrix}275&16\\42&45\end{bmatrix}$, $\begin{bmatrix}277&24\\72&13\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.0.ck.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $15482880$ |
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 |
---|---|---|---|---|---|
40.48.0-40.i.2.30 | $40$ | $2$ | $2$ | $0$ | $0$ |
56.48.0-56.m.1.17 | $56$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-40.i.2.18 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.m.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.t.2.50 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.t.2.64 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.z.2.11 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.bd.2.9 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.cr.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.cu.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.fa.1.8 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.fb.1.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.fe.2.13 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ff.2.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.iw.2.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ix.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jg.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jh.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kc.1.8 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kd.1.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.km.2.10 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kn.2.14 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.de.2.28 | $280$ | $5$ | $5$ | $16$ |