Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | ||||
| Index: | $12$ | $\PSL_2$-index: | $6$ | ||||
| Genus: | $0 = 1 + \frac{ 6 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 3 }{2}$ | ||||||
| Cusps: | $3$ (all of which are rational) | Cusp widths | $1^{2}\cdot4$ | Cusp orbits | $1^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $3$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4B0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}35&102\\264&113\end{bmatrix}$, $\begin{bmatrix}80&117\\63&278\end{bmatrix}$, $\begin{bmatrix}111&86\\146&39\end{bmatrix}$, $\begin{bmatrix}113&146\\102&273\end{bmatrix}$, $\begin{bmatrix}163&106\\80&273\end{bmatrix}$, $\begin{bmatrix}188&157\\265&72\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 4.6.0.c.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $123863040$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 95098 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 6 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{x^{6}(48x^{2}-y^{2})^{3}}{x^{10}(8x-y)(8x+y)}$ |
Modular covers
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.24.0-4.b.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-4.d.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.d.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-20.g.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-28.g.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-140.g.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-20.h.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-28.h.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-140.h.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.k.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.m.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.m.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.n.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.n.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.o.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.o.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.p.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-8.p.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.s.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.s.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.s.1.13 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.v.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.v.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.v.1.13 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.y.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.y.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.y.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.y.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.y.1.25 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.y.1.29 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.z.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.z.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.z.1.10 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.z.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.z.1.19 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.z.1.27 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.ba.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.ba.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.ba.1.10 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.ba.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.ba.1.19 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.ba.1.27 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.bb.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-40.bb.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.bb.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-56.bb.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.bb.1.25 | $280$ | $2$ | $2$ | $0$ |
| 280.24.0-280.bb.1.29 | $280$ | $2$ | $2$ | $0$ |
| 280.60.2-20.c.1.7 | $280$ | $5$ | $5$ | $2$ |
| 280.72.1-20.c.1.21 | $280$ | $6$ | $6$ | $1$ |
| 280.96.2-28.c.1.28 | $280$ | $8$ | $8$ | $2$ |
| 280.120.3-20.c.1.12 | $280$ | $10$ | $10$ | $3$ |
| 280.252.7-28.c.1.24 | $280$ | $21$ | $21$ | $7$ |
| 280.336.9-28.c.1.18 | $280$ | $28$ | $28$ | $9$ |