Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20H3 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}11&50\\94&89\end{bmatrix}$, $\begin{bmatrix}123&80\\58&51\end{bmatrix}$, $\begin{bmatrix}209&50\\245&229\end{bmatrix}$, $\begin{bmatrix}241&240\\80&29\end{bmatrix}$, $\begin{bmatrix}261&270\\5&153\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.72.3.u.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $32$ |
| Cyclic 280-torsion field degree: | $3072$ |
| Full 280-torsion field degree: | $10321920$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.72.1-20.b.1.9 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 280.72.1-20.b.1.5 | $280$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.288.5-140.k.2.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-140.y.1.3 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-140.bx.2.2 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-140.by.2.1 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-140.cf.1.4 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-140.cg.2.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-140.cn.2.3 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-140.co.2.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.cy.2.7 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.gq.1.6 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.nc.2.8 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.no.2.4 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.pl.1.4 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.ps.2.3 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.rp.2.4 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.rw.2.4 | $280$ | $2$ | $2$ | $5$ |