Invariants
Level: | $280$ | $\SL_2$-level: | $20$ | 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 | $2^{6}\cdot10^{6}$ | Cusp orbits | $2^{6}$ | ||
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: | 10K1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}5&226\\14&263\end{bmatrix}$, $\begin{bmatrix}31&42\\42&171\end{bmatrix}$, $\begin{bmatrix}163&60\\16&219\end{bmatrix}$, $\begin{bmatrix}193&224\\204&43\end{bmatrix}$, $\begin{bmatrix}217&276\\96&37\end{bmatrix}$, $\begin{bmatrix}249&152\\42&29\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.72.1.a.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $32$ |
Cyclic 280-torsion field degree: | $3072$ |
Full 280-torsion field degree: | $10321920$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
40.72.1-10.a.1.1 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
140.72.1-10.a.1.4 | $140$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.288.5-280.z.1.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.z.1.19 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ba.1.3 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ba.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ba.1.16 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bc.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bc.1.27 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bc.1.47 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bd.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bd.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bd.1.14 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bl.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bl.1.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bl.1.13 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bm.1.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bm.1.5 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bm.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bo.1.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bo.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bo.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bp.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bp.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bp.1.14 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bx.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bx.1.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bx.1.13 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.by.1.3 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.by.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.by.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ca.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ca.1.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ca.1.11 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cb.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cb.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cb.1.16 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cj.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cj.1.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cj.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ck.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ck.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.ck.1.14 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cm.1.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cm.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cm.1.11 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cn.1.2 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cn.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cn.1.16 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |