Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}33&268\\144&27\end{bmatrix}$, $\begin{bmatrix}45&196\\262&251\end{bmatrix}$, $\begin{bmatrix}69&180\\252&201\end{bmatrix}$, $\begin{bmatrix}81&248\\8&165\end{bmatrix}$, $\begin{bmatrix}251&40\\144&69\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 280.192.1-280.gm.1.1, 280.192.1-280.gm.1.2, 280.192.1-280.gm.1.3, 280.192.1-280.gm.1.4, 280.192.1-280.gm.1.5, 280.192.1-280.gm.1.6, 280.192.1-280.gm.1.7, 280.192.1-280.gm.1.8, 280.192.1-280.gm.1.9, 280.192.1-280.gm.1.10, 280.192.1-280.gm.1.11, 280.192.1-280.gm.1.12, 280.192.1-280.gm.1.13, 280.192.1-280.gm.1.14, 280.192.1-280.gm.1.15, 280.192.1-280.gm.1.16 |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $15482880$ |
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 |
---|---|---|---|---|---|---|
40.48.0.k.2 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.48.1.bi.2 | $56$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
280.48.0.i.2 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0.bp.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0.bt.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.1.bu.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.48.1.dk.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |