Invariants
Level: | $132$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
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: | 12P1 |
Level structure
$\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}33&38\\86&9\end{bmatrix}$, $\begin{bmatrix}55&36\\84&31\end{bmatrix}$, $\begin{bmatrix}85&6\\36&13\end{bmatrix}$, $\begin{bmatrix}95&78\\20&79\end{bmatrix}$, $\begin{bmatrix}117&4\\80&55\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 132.48.1.a.1 for the level structure with $-I$) |
Cyclic 132-isogeny field degree: | $24$ |
Cyclic 132-torsion field degree: | $960$ |
Full 132-torsion field degree: | $633600$ |
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 |
---|---|---|---|---|---|---|
12.48.0-6.a.1.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
66.48.0-6.a.1.2 | $66$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
132.48.0-132.n.1.8 | $132$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
132.48.0-132.n.1.9 | $132$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
132.48.1-132.p.1.8 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.48.1-132.p.1.9 | $132$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
132.192.1-132.e.1.7 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.192.1-132.e.2.7 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.192.1-132.e.3.5 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.192.1-132.e.4.5 | $132$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
132.192.3-132.a.1.8 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.192.3-132.c.1.12 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.192.3-132.g.1.12 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.192.3-132.i.1.14 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.192.3-132.o.1.12 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.192.3-132.o.2.4 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.192.3-132.s.1.8 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.192.3-132.s.2.4 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
132.288.5-132.a.1.5 | $132$ | $3$ | $3$ | $5$ | $?$ | not computed |
264.192.1-264.ln.1.12 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ln.2.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ln.3.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ln.4.12 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.3-264.cr.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cv.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.df.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dl.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.en.1.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.en.2.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fg.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fg.2.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |