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 | $2^{5}$ | ||
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: | $\begin{bmatrix}123&88\\182&169\end{bmatrix}$, $\begin{bmatrix}127&184\\70&169\end{bmatrix}$, $\begin{bmatrix}133&176\\132&183\end{bmatrix}$, $\begin{bmatrix}265&16\\166&85\end{bmatrix}$, $\begin{bmatrix}273&88\\250&63\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.48.0.bb.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $48$ |
Cyclic 280-torsion field degree: | $4608$ |
Full 280-torsion field degree: | $15482880$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 7 x^{2} + 7 y^{2} + 8 z^{2} $ |
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.i.1.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-8.i.1.11 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.i.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.i.1.16 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.bv.1.8 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.bv.1.9 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
280.192.1-56.q.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.br.1.3 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.cc.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.cg.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kz.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ld.2.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.pb.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.pj.2.10 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.eb.1.21 | $280$ | $5$ | $5$ | $16$ |