Invariants
Level: | $132$ | $\SL_2$-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 | $2^{6}\cdot4$ | ||
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
$\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}53&54\\54&47\end{bmatrix}$, $\begin{bmatrix}101&54\\56&65\end{bmatrix}$, $\begin{bmatrix}115&66\\86&101\end{bmatrix}$, $\begin{bmatrix}131&72\\70&83\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 132.96.1.g.4 for the level structure with $-I$) |
Cyclic 132-isogeny field degree: | $24$ |
Cyclic 132-torsion field degree: | $480$ |
Full 132-torsion field degree: | $316800$ |
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 |
---|---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
132.96.0-12.a.2.15 | $132$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
132.96.0-132.a.2.9 | $132$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
132.96.0-132.a.2.23 | $132$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
132.96.1-132.c.1.8 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.c.1.12 | $132$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
132.384.5-132.i.2.2 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.384.5-132.k.4.6 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.384.5-132.l.4.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.384.5-132.o.3.6 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.384.5-132.s.2.4 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.384.5-132.u.4.5 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.384.5-132.v.4.2 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.384.5-132.y.2.5 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jg.1.12 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jq.1.12 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.jy.4.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.kt.4.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.os.4.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.pc.4.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.pk.1.12 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.qf.1.12 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |