Invariants
Level: | $132$ | $\SL_2$-level: | $12$ | 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: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12F1 |
Level structure
$\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}44&63\\57&26\end{bmatrix}$, $\begin{bmatrix}49&116\\30&89\end{bmatrix}$, $\begin{bmatrix}85&44\\102&23\end{bmatrix}$, $\begin{bmatrix}129&116\\106&89\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 132.24.1.m.1 for the level structure with $-I$) |
Cyclic 132-isogeny field degree: | $24$ |
Cyclic 132-torsion field degree: | $960$ |
Full 132-torsion field degree: | $1267200$ |
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 |
---|---|---|---|---|---|---|
6.24.0-6.a.1.3 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
132.24.0-6.a.1.11 | $132$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
132.96.1-132.d.1.17 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.f.1.1 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.n.1.1 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.o.1.8 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.r.1.5 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.s.1.1 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.v.1.1 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.96.1-132.w.1.5 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.144.3-132.jx.1.4 | $132$ | $3$ | $3$ | $3$ | $?$ | not computed |
264.96.1-264.gj.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.kb.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.zl.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.zo.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.baf.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bai.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bar.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.bau.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |