Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}19&4\\38&35\end{bmatrix}$, $\begin{bmatrix}25&16\\116&29\end{bmatrix}$, $\begin{bmatrix}125&116\\21&115\end{bmatrix}$, $\begin{bmatrix}137&100\\82&61\end{bmatrix}$, $\begin{bmatrix}203&32\\199&157\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 280.96.1-280.ne.1.1, 280.96.1-280.ne.1.2, 280.96.1-280.ne.1.3, 280.96.1-280.ne.1.4, 280.96.1-280.ne.1.5, 280.96.1-280.ne.1.6, 280.96.1-280.ne.1.7, 280.96.1-280.ne.1.8 |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $30965760$ |
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 |
---|---|---|---|---|---|---|
40.24.0.be.1 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.24.1.n.1 | $56$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
280.24.0.bl.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.24.0.mg.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.24.0.mh.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.24.1.ii.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.24.1.ij.1 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.240.17.uc.1 | $280$ | $5$ | $5$ | $17$ | $?$ | not computed |
280.288.17.cmm.1 | $280$ | $6$ | $6$ | $17$ | $?$ | not computed |