Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1568$ | ||
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: | $\begin{bmatrix}17&176\\176&27\end{bmatrix}$, $\begin{bmatrix}55&138\\84&223\end{bmatrix}$, $\begin{bmatrix}71&188\\148&113\end{bmatrix}$, $\begin{bmatrix}115&4\\176&271\end{bmatrix}$, $\begin{bmatrix}233&106\\252&121\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.48.1.bf.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: | 1568.2.a.e |
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.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.48.0-8.e.1.11 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-56.i.2.11 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-56.i.2.20 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.1-56.c.1.11 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.48.1-56.c.1.20 | $280$ | $2$ | $2$ | $1$ | $?$ | 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.s.2.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.x.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.bf.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.bh.2.3 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.bx.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.bz.2.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.cc.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-56.cd.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ga.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ge.1.9 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.hh.1.9 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.hl.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.lp.1.9 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.lt.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.mv.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.mz.1.9 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.480.17-280.ep.2.10 | $280$ | $5$ | $5$ | $17$ | $?$ | not computed |