Invariants
Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 72$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20H1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}34&217\\67&264\end{bmatrix}$, $\begin{bmatrix}85&156\\208&173\end{bmatrix}$, $\begin{bmatrix}170&87\\267&60\end{bmatrix}$, $\begin{bmatrix}204&193\\251&226\end{bmatrix}$, $\begin{bmatrix}206&275\\109&192\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.72.1.d.2 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $32$ |
Cyclic 280-torsion field degree: | $3072$ |
Full 280-torsion field degree: | $10321920$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
40.72.1-20.b.1.9 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
280.72.1-20.b.1.16 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
280.288.5-140.i.1.10 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-140.y.1.3 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-140.bw.1.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-140.by.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cu.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-140.cv.1.3 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-140.cw.1.3 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-140.dd.1.3 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-140.de.1.3 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.gp.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.na.1.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.nn.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.xk.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.xr.1.5 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.zo.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.zv.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |