Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
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: | 8B1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}67&16\\138&77\end{bmatrix}$, $\begin{bmatrix}69&270\\76&233\end{bmatrix}$, $\begin{bmatrix}197&18\\250&63\end{bmatrix}$, $\begin{bmatrix}233&86\\132&193\end{bmatrix}$, $\begin{bmatrix}245&46\\142&251\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.24.1.b.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $192$ |
Cyclic 280-torsion field degree: | $18432$ |
Full 280-torsion field degree: | $30965760$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 |
---|---|---|---|---|---|---|
40.24.0-4.a.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.24.0-4.a.1.4 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
280.96.1-280.a.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.d.1.3 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.n.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.z.1.3 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.ci.1.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.cl.1.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.cu.1.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.cx.1.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.ee.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.eh.1.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.eq.1.5 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.et.1.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.fc.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.ff.1.5 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.fh.1.7 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.96.1-280.fj.1.5 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.240.9-280.f.1.14 | $280$ | $5$ | $5$ | $9$ | $?$ | not computed |
280.288.9-280.f.1.25 | $280$ | $6$ | $6$ | $9$ | $?$ | not computed |
280.384.13-280.f.1.29 | $280$ | $8$ | $8$ | $13$ | $?$ | not computed |
280.480.17-280.ft.1.30 | $280$ | $10$ | $10$ | $17$ | $?$ | not computed |