Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $32$ | ||
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: | $\begin{bmatrix}15&192\\78&173\end{bmatrix}$, $\begin{bmatrix}111&80\\80&143\end{bmatrix}$, $\begin{bmatrix}233&4\\76&267\end{bmatrix}$, $\begin{bmatrix}273&32\\264&269\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.y.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $7741440$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 32.2.a.a |
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 |
---|---|---|---|---|---|---|
40.96.1-8.k.2.4 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
280.96.0-56.i.2.13 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.i.2.16 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.j.2.1 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.j.2.11 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.u.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.u.1.15 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.v.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.v.1.15 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.1-8.k.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.p.1.14 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.p.1.15 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.q.2.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.q.2.14 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |