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Properties

Label 132.48.1.l.1
Level $132$
Index $48$
Genus $1$
Cusps $8$
$\Q$-cusps $4$

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Invariants

Level: $132$ $\SL_2$-level: $12$ Newform level: $1$
Index: $48$ $\PSL_2$-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: $\begin{bmatrix}43&2\\12&83\end{bmatrix}$, $\begin{bmatrix}81&74\\116&63\end{bmatrix}$, $\begin{bmatrix}93&82\\20&13\end{bmatrix}$, $\begin{bmatrix}107&129\\36&59\end{bmatrix}$, $\begin{bmatrix}111&124\\88&105\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 132.96.1-132.l.1.1, 132.96.1-132.l.1.2, 132.96.1-132.l.1.3, 132.96.1-132.l.1.4, 132.96.1-132.l.1.5, 132.96.1-132.l.1.6, 132.96.1-132.l.1.7, 132.96.1-132.l.1.8, 132.96.1-132.l.1.9, 132.96.1-132.l.1.10, 132.96.1-132.l.1.11, 132.96.1-132.l.1.12, 264.96.1-132.l.1.1, 264.96.1-132.l.1.2, 264.96.1-132.l.1.3, 264.96.1-132.l.1.4, 264.96.1-132.l.1.5, 264.96.1-132.l.1.6, 264.96.1-132.l.1.7, 264.96.1-132.l.1.8, 264.96.1-132.l.1.9, 264.96.1-132.l.1.10, 264.96.1-132.l.1.11, 264.96.1-132.l.1.12, 264.96.1-132.l.1.13, 264.96.1-132.l.1.14, 264.96.1-132.l.1.15, 264.96.1-132.l.1.16, 264.96.1-132.l.1.17, 264.96.1-132.l.1.18, 264.96.1-132.l.1.19, 264.96.1-132.l.1.20, 264.96.1-132.l.1.21, 264.96.1-132.l.1.22, 264.96.1-132.l.1.23, 264.96.1-132.l.1.24, 264.96.1-132.l.1.25, 264.96.1-132.l.1.26, 264.96.1-132.l.1.27, 264.96.1-132.l.1.28
Cyclic 132-isogeny field degree: $12$
Cyclic 132-torsion field degree: $480$
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

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve Level Index Degree Genus Rank Kernel decomposition
$X_0(3)$ $3$ $12$ $12$ $0$ $0$ full Jacobian
44.12.0.h.1 $44$ $4$ $4$ $0$ $0$ full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
$X_0(12)$ $12$ $2$ $2$ $0$ $0$ full Jacobian
44.12.0.h.1 $44$ $4$ $4$ $0$ $0$ full Jacobian
132.24.0.m.1 $132$ $2$ $2$ $0$ $?$ full Jacobian
132.24.1.p.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
132.96.1.m.1 $132$ $2$ $2$ $1$ $?$ dimension zero
132.96.1.m.2 $132$ $2$ $2$ $1$ $?$ dimension zero
132.96.1.m.3 $132$ $2$ $2$ $1$ $?$ dimension zero
132.96.1.m.4 $132$ $2$ $2$ $1$ $?$ dimension zero
132.144.5.cb.1 $132$ $3$ $3$ $5$ $?$ not computed
264.96.1.rs.1 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.rs.2 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.rs.3 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.rs.4 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.3.ku.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.ku.2 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.kw.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.kw.2 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.ls.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.lt.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.ma.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.mb.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.mm.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.mn.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.mq.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.mr.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.om.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.om.2 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.oo.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.oo.2 $264$ $2$ $2$ $3$ $?$ not computed