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: | $\begin{bmatrix}51&200\\22&159\end{bmatrix}$, $\begin{bmatrix}85&156\\172&241\end{bmatrix}$, $\begin{bmatrix}165&132\\136&219\end{bmatrix}$, $\begin{bmatrix}167&76\\92&5\end{bmatrix}$, $\begin{bmatrix}233&132\\140&73\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.48.0.p.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
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 56 x^{2} + y^{2} + 14 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.d.1.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-8.d.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.i.2.7 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.i.2.9 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.l.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-56.l.1.6 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.a.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.d.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.r.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.u.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.ba.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.bb.2.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.be.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-56.bf.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ie.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.if.1.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ik.1.8 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.il.1.8 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jk.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jl.1.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jq.1.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jr.1.4 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.cu.2.30 | $280$ | $5$ | $5$ | $16$ |