Invariants
Level: | $264$ | $\SL_2$-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
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}71&42\\240&155\end{bmatrix}$, $\begin{bmatrix}73&239\\116&111\end{bmatrix}$, $\begin{bmatrix}83&228\\32&191\end{bmatrix}$, $\begin{bmatrix}111&260\\80&11\end{bmatrix}$, $\begin{bmatrix}133&176\\180&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.24.1.n.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
Full 264-torsion field degree: | $20275200$ |
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 |
---|---|---|---|---|---|---|
8.24.0-4.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
132.24.0-4.d.1.2 | $132$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.96.1-264.iv.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.iy.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.jg.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.jn.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.ki.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.kp.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.ky.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.lj.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.mh.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.mm.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.nn.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.no.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.od.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.oe.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.or.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.os.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.144.5-264.bz.1.4 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |
264.192.5-264.bf.1.8 | $264$ | $4$ | $4$ | $5$ | $?$ | not computed |