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: | 20J3 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}71&50\\144&101\end{bmatrix}$, $\begin{bmatrix}133&150\\262&71\end{bmatrix}$, $\begin{bmatrix}141&50\\213&21\end{bmatrix}$, $\begin{bmatrix}169&180\\105&33\end{bmatrix}$, $\begin{bmatrix}181&170\\245&209\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.72.3.n.1 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 | $40$ | $2$ | $2$ | $1$ | $0$ |
280.24.0-28.f.1.4 | $280$ | $6$ | $6$ | $0$ | $?$ |
280.72.1-20.b.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ |
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.cf.1.4 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.cf.2.4 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.ch.1.8 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.ch.2.8 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.cv.1.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.cv.2.2 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.cx.1.6 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.cx.2.4 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.pk.1.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.pk.2.2 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.py.1.2 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.py.2.2 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.xj.1.5 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.xj.2.2 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.xx.1.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.xx.2.2 | $280$ | $2$ | $2$ | $5$ |