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 | $4^{2}$ | ||
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: | $\begin{bmatrix}129&158\\1&123\end{bmatrix}$, $\begin{bmatrix}159&234\\148&157\end{bmatrix}$, $\begin{bmatrix}183&86\\219&205\end{bmatrix}$, $\begin{bmatrix}269&236\\6&121\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 280-isogeny field degree: | $192$ |
Cyclic 280-torsion field degree: | $18432$ |
Full 280-torsion field degree: | $30965760$ |
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 |
---|---|---|---|---|---|---|
40.24.1.dv.1 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
56.24.0.dy.1 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.24.0.ii.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.24.0.ir.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.24.0.lv.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.24.1.eq.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.24.1.gi.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.cmn.1 | $280$ | $5$ | $5$ | $17$ | $?$ | not computed |
280.288.17.imn.1 | $280$ | $6$ | $6$ | $17$ | $?$ | not computed |