Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
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 | $2^{2}\cdot4^{3}$ | ||
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: | $\begin{bmatrix}55&8\\196&79\end{bmatrix}$, $\begin{bmatrix}89&76\\192&185\end{bmatrix}$, $\begin{bmatrix}163&232\\72&77\end{bmatrix}$, $\begin{bmatrix}219&240\\268&97\end{bmatrix}$, $\begin{bmatrix}273&200\\276&257\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.96.1.a.2 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: | not computed |
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.a.1.6 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.96.0-8.a.1.2 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.96.0-280.b.1.14 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-280.b.1.27 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-280.bo.2.15 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-280.bo.2.18 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-280.bq.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.0-280.bq.1.27 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.96.1-280.n.2.14 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.n.2.27 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.dw.1.9 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.dw.1.20 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.dy.1.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.dy.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.384.5-280.a.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.c.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.d.2.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.g.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.h.2.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.k.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.l.2.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.384.5-280.r.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |