Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $4$ are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $1^{4}\cdot2$ | ||
| 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: | 8G0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}29&176\\182&79\end{bmatrix}$, $\begin{bmatrix}61&272\\34&151\end{bmatrix}$, $\begin{bmatrix}127&8\\184&273\end{bmatrix}$, $\begin{bmatrix}185&224\\266&99\end{bmatrix}$, $\begin{bmatrix}193&88\\160&143\end{bmatrix}$, $\begin{bmatrix}277&96\\14&45\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 8.24.0.i.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $48$ |
| Cyclic 280-torsion field degree: | $4608$ |
| Full 280-torsion field degree: | $30965760$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 122 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 24 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{x^{24}(x^{8}+240x^{6}y^{2}+2144x^{4}y^{4}+3840x^{2}y^{6}+256y^{8})^{3}}{y^{2}x^{26}(x-2y)^{8}(x+2y)^{8}(x^{2}+4y^{2})^{2}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 280.24.0-4.b.1.8 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.24.0-8.n.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.96.0-8.j.1.5 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-8.j.2.3 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-8.k.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-8.k.2.8 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-8.l.1.6 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-8.l.2.1 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-56.z.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-56.z.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-56.ba.1.10 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-56.ba.2.12 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-40.bb.1.5 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-40.bb.2.5 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-56.bb.1.1 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-56.bb.2.6 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-40.bc.1.16 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-40.bc.2.14 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-40.bd.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-40.bd.2.3 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.cx.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.cx.2.3 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.cy.1.25 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.cy.2.26 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.cz.1.9 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.cz.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.1-8.h.1.6 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-8.p.1.7 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-40.bu.1.10 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-56.bu.1.6 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-40.bv.1.2 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-56.bv.1.2 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.fm.1.18 | $280$ | $2$ | $2$ | $1$ |
| 280.96.1-280.fn.1.21 | $280$ | $2$ | $2$ | $1$ |
| 280.240.8-40.v.1.7 | $280$ | $5$ | $5$ | $8$ |
| 280.288.7-40.br.1.11 | $280$ | $6$ | $6$ | $7$ |
| 280.384.11-56.bn.1.30 | $280$ | $8$ | $8$ | $11$ |
| 280.480.15-40.ch.1.32 | $280$ | $10$ | $10$ | $15$ |