Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}49&120\\218&245\end{bmatrix}$, $\begin{bmatrix}115&114\\36&203\end{bmatrix}$, $\begin{bmatrix}145&138\\176&97\end{bmatrix}$, $\begin{bmatrix}169&72\\172&215\end{bmatrix}$, $\begin{bmatrix}229&6\\66&167\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.1.lo.4 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $5068800$ |
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 |
---|---|---|---|---|---|---|
24.96.0-24.o.1.31 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
132.96.0-132.a.2.32 | $132$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-132.a.2.7 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-24.o.1.10 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.1-264.dg.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.dg.1.21 | $264$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.384.5-264.ip.1.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.iq.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ja.3.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jb.2.15 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jy.2.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jz.2.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.km.2.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.kn.3.12 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.oa.1.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.od.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ok.1.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.op.2.6 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.pi.2.11 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.pn.2.14 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.pw.4.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.qb.4.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |