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: | $\begin{bmatrix}83&90\\216&137\end{bmatrix}$, $\begin{bmatrix}119&200\\185&187\end{bmatrix}$, $\begin{bmatrix}183&260\\237&107\end{bmatrix}$, $\begin{bmatrix}193&30\\193&129\end{bmatrix}$, $\begin{bmatrix}207&40\\239&179\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.72.3.q.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 no real points, and therefore no 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 | $40$ | $2$ | $2$ | $1$ | $0$ |
280.24.0-140.e.1.4 | $280$ | $6$ | $6$ | $0$ | $?$ |
280.72.1-20.b.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ |
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.cm.1.12 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.cm.2.10 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.co.1.8 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.co.2.6 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.dc.1.6 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.dc.2.2 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.de.1.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-140.de.2.1 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.rh.1.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.rh.2.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.rv.1.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.rv.2.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.zg.1.5 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.zg.2.3 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.zu.1.5 | $280$ | $2$ | $2$ | $5$ |
280.288.5-280.zu.2.3 | $280$ | $2$ | $2$ | $5$ |