Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4E0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}57&220\\158&43\end{bmatrix}$, $\begin{bmatrix}57&236\\198&145\end{bmatrix}$, $\begin{bmatrix}77&192\\132&219\end{bmatrix}$, $\begin{bmatrix}123&172\\204&39\end{bmatrix}$, $\begin{bmatrix}179&36\\222&239\end{bmatrix}$, $\begin{bmatrix}237&4\\268&179\end{bmatrix}$, $\begin{bmatrix}239&92\\188&147\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 4.12.0.b.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $61931520$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 2569 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 12 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{x^{12}(256x^{4}-16x^{2}y^{2}+y^{4})^{3}}{y^{4}x^{16}(4x-y)^{2}(4x+y)^{2}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 280.12.0-4.c.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.12.0-4.c.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 |
|---|---|---|---|---|
| 280.48.0-4.b.1.5 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.c.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-20.c.1.14 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-28.c.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-140.c.1.26 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.d.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.d.1.11 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.d.2.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.d.2.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.e.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.e.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.e.2.5 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.e.2.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.e.1.18 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.e.1.20 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.e.1.34 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.h.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.h.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.h.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.h.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.h.2.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.h.2.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.h.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.h.1.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.h.2.15 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.h.2.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.i.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.i.1.11 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.i.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.i.1.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.i.2.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.i.2.14 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.i.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.i.1.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.i.2.15 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.i.2.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.l.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.l.1.11 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.l.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.l.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.m.1.5 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.m.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.m.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.m.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.t.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.t.1.32 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.t.2.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.t.2.29 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.u.1.13 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.u.1.24 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.u.2.4 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.u.2.31 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.x.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.x.1.24 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.y.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.y.1.20 | $280$ | $2$ | $2$ | $0$ |
| 280.48.1-8.c.1.6 | $280$ | $2$ | $2$ | $1$ |
| 280.48.1-40.c.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.48.1-56.c.1.13 | $280$ | $2$ | $2$ | $1$ |
| 280.48.1-280.c.1.28 | $280$ | $2$ | $2$ | $1$ |
| 280.48.1-8.d.1.7 | $280$ | $2$ | $2$ | $1$ |
| 280.48.1-40.d.1.14 | $280$ | $2$ | $2$ | $1$ |
| 280.48.1-56.d.1.18 | $280$ | $2$ | $2$ | $1$ |
| 280.48.1-280.d.1.28 | $280$ | $2$ | $2$ | $1$ |
| 280.120.4-20.b.1.20 | $280$ | $5$ | $5$ | $4$ |
| 280.144.3-20.b.1.17 | $280$ | $6$ | $6$ | $3$ |
| 280.192.5-28.b.1.28 | $280$ | $8$ | $8$ | $5$ |
| 280.240.7-20.b.1.35 | $280$ | $10$ | $10$ | $7$ |
| 280.504.16-28.b.1.43 | $280$ | $21$ | $21$ | $16$ |