Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $3136$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}35&16\\232&133\end{bmatrix}$, $\begin{bmatrix}89&68\\168&115\end{bmatrix}$, $\begin{bmatrix}149&262\\56&111\end{bmatrix}$, $\begin{bmatrix}199&240\\80&197\end{bmatrix}$, $\begin{bmatrix}261&36\\244&13\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.48.1.bj.2 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: | 3136.2.a.m |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.48.0-8.e.1.8 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.48.0-8.e.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-56.i.1.16 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-56.i.1.32 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.1-56.d.1.14 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.48.1-56.d.1.18 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.192.1-56.r.1.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.w.1.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.bn.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.bp.1.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.bw.1.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.by.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.cg.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.ch.1.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.gq.2.15 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.gu.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.hx.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ib.2.15 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.me.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.mi.2.13 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.nk.2.13 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.no.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.480.17-280.ex.2.8 | $280$ | $5$ | $5$ | $17$ | $?$ | not computed |