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: | $\begin{bmatrix}9&224\\18&201\end{bmatrix}$, $\begin{bmatrix}81&4\\206&127\end{bmatrix}$, $\begin{bmatrix}241&212\\114&51\end{bmatrix}$, $\begin{bmatrix}255&116\\254&177\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.cg.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 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 |
---|---|---|---|---|---|---|
40.96.0-8.k.1.7 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.96.0-8.k.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.l.2.8 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.l.2.16 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.n.2.8 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.n.2.16 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.bb.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.bb.1.12 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.1-56.bh.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bh.2.16 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bj.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bj.2.16 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bv.1.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bv.1.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |