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: | $\begin{bmatrix}17&24\\228&229\end{bmatrix}$, $\begin{bmatrix}29&152\\48&151\end{bmatrix}$, $\begin{bmatrix}65&188\\124&179\end{bmatrix}$, $\begin{bmatrix}69&268\\20&161\end{bmatrix}$, $\begin{bmatrix}75&204\\12&3\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.r.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: | 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.b.1.11 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.96.0-8.b.1.6 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.c.1.6 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.c.1.10 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.p.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.p.1.16 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.r.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-56.r.1.16 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.1-56.n.2.9 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.n.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bh.2.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bh.2.15 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bj.2.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-56.bj.2.16 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.384.5-56.p.2.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-56.s.2.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-56.t.1.4 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-56.v.2.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.fn.1.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.fp.2.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.fu.1.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.fw.2.8 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |