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 | $1^{2}\cdot2\cdot8$ | 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: | 8C0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}8&219\\129&274\end{bmatrix}$, $\begin{bmatrix}179&22\\238&187\end{bmatrix}$, $\begin{bmatrix}205&74\\162&181\end{bmatrix}$, $\begin{bmatrix}223&58\\140&237\end{bmatrix}$, $\begin{bmatrix}227&274\\8&13\end{bmatrix}$, $\begin{bmatrix}276&171\\205&42\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 8.12.0.n.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $48$ |
| Cyclic 280-torsion field degree: | $4608$ |
| 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 5199 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 12 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{x^{12}(x^{4}-16x^{2}y^{2}+16y^{4})^{3}}{y^{8}x^{14}(x-4y)(x+4y)}$ |
Modular covers
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.48.0-8.i.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.k.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.q.1.5 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.r.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.ba.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.ba.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.ba.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.ba.2.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.bb.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.bb.1.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.bb.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-8.bb.2.7 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bf.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bh.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.bj.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bj.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.bl.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bl.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.bn.1.8 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.bp.1.11 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bu.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bu.1.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bu.2.5 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bu.2.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bv.1.5 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bv.1.12 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bv.2.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-56.bv.2.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.ca.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.ca.1.11 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.ca.2.3 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.ca.2.14 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.cb.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.cb.1.14 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.cb.2.6 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-40.cb.2.11 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.dd.1.20 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.df.1.23 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.dh.1.16 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.dj.1.23 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ei.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ei.1.32 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ei.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ei.2.31 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ej.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ej.1.31 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ej.2.1 | $280$ | $2$ | $2$ | $0$ |
| 280.48.0-280.ej.2.32 | $280$ | $2$ | $2$ | $0$ |
| 280.120.4-40.bl.1.4 | $280$ | $5$ | $5$ | $4$ |
| 280.144.3-40.bx.1.14 | $280$ | $6$ | $6$ | $3$ |
| 280.192.5-56.bl.1.25 | $280$ | $8$ | $8$ | $5$ |
| 280.240.7-40.cj.1.6 | $280$ | $10$ | $10$ | $7$ |
| 280.504.16-56.cj.1.31 | $280$ | $21$ | $21$ | $16$ |