Invariants
Level: | $132$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $3^{8}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
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: | 12S1 |
Level structure
$\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}35&40\\114&109\end{bmatrix}$, $\begin{bmatrix}47&22\\114&91\end{bmatrix}$, $\begin{bmatrix}55&104\\72&5\end{bmatrix}$, $\begin{bmatrix}83&24\\66&113\end{bmatrix}$, $\begin{bmatrix}119&88\\75&19\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 132.144.1-132.p.1.1, 132.144.1-132.p.1.2, 132.144.1-132.p.1.3, 132.144.1-132.p.1.4, 132.144.1-132.p.1.5, 132.144.1-132.p.1.6, 132.144.1-132.p.1.7, 132.144.1-132.p.1.8, 264.144.1-132.p.1.1, 264.144.1-132.p.1.2, 264.144.1-132.p.1.3, 264.144.1-132.p.1.4, 264.144.1-132.p.1.5, 264.144.1-132.p.1.6, 264.144.1-132.p.1.7, 264.144.1-132.p.1.8 |
Cyclic 132-isogeny field degree: | $24$ |
Cyclic 132-torsion field degree: | $960$ |
Full 132-torsion field degree: | $844800$ |
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 |
---|---|---|---|---|---|---|
6.36.0.a.1 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
132.24.0.q.1 | $132$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
132.36.0.c.1 | $132$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
132.36.1.ca.1 | $132$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
132.144.5.f.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.144.5.be.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.144.5.dk.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.144.5.do.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.144.5.fw.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.144.5.ge.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.144.5.gu.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
132.144.5.gz.1 | $132$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.dt.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.ig.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.bbn.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.bcp.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.bsq.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.buu.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.bzc.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.144.5.cal.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |