Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $3136$ | ||
Index: | $192$ | $\PSL_2$-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 | $2^{4}\cdot4^{2}$ | ||
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: | $\begin{bmatrix}31&128\\194&89\end{bmatrix}$, $\begin{bmatrix}147&208\\214&137\end{bmatrix}$, $\begin{bmatrix}181&264\\276&123\end{bmatrix}$, $\begin{bmatrix}269&168\\70&279\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.cf.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $48$ |
Cyclic 280-torsion field degree: | $4608$ |
Full 280-torsion field degree: | $7741440$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 3136.2.a.m |
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 |
---|---|---|---|---|---|---|
40.96.0-8.k.2.2 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.96.0-8.k.2.7 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.k.1.2 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.k.1.9 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.m.1.3 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.m.1.9 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.z.1.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.z.1.9 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.1-56.bg.2.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bg.2.3 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bi.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bi.1.9 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bv.1.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bv.1.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |