Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}89&30\\0&223\end{bmatrix}$, $\begin{bmatrix}157&136\\196&95\end{bmatrix}$, $\begin{bmatrix}223&216\\256&21\end{bmatrix}$, $\begin{bmatrix}255&178\\132&151\end{bmatrix}$, $\begin{bmatrix}275&166\\208&85\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.1.cg.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $15482880$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 |
---|---|---|---|---|---|---|
40.48.1-40.d.1.12 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
56.48.0-56.i.1.31 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.48.0-56.i.1.16 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-280.t.2.8 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-280.t.2.56 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.1-40.d.1.14 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.192.1-280.w.2.3 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ci.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.fj.2.16 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.fn.2.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.gy.2.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.hk.2.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ho.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ia.2.15 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.jk.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.jw.2.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ka.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.km.2.14 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.kq.2.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ku.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.lb.2.16 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ld.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.480.17-280.di.1.24 | $280$ | $5$ | $5$ | $17$ | $?$ | not computed |