Invariants
Level: | $132$ | $\SL_2$-level: | $12$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{3}\cdot6^{3}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 6I0 |
Level structure
$\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}40&15\\19&98\end{bmatrix}$, $\begin{bmatrix}41&88\\128&15\end{bmatrix}$, $\begin{bmatrix}56&51\\57&38\end{bmatrix}$, $\begin{bmatrix}100&17\\51&104\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 132.24.0.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: | $1267200$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.24.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ |
132.24.0-6.a.1.9 | $132$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
132.96.1-132.j.1.1 | $132$ | $2$ | $2$ | $1$ |
132.96.1-132.l.1.6 | $132$ | $2$ | $2$ | $1$ |
132.96.1-132.v.1.5 | $132$ | $2$ | $2$ | $1$ |
132.96.1-132.x.1.4 | $132$ | $2$ | $2$ | $1$ |
132.96.1-132.bh.1.2 | $132$ | $2$ | $2$ | $1$ |
132.96.1-132.bj.1.2 | $132$ | $2$ | $2$ | $1$ |
132.96.1-132.bp.1.3 | $132$ | $2$ | $2$ | $1$ |
132.96.1-132.br.1.12 | $132$ | $2$ | $2$ | $1$ |
132.144.1-132.h.1.8 | $132$ | $3$ | $3$ | $1$ |
264.96.1-264.yy.1.3 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.ze.1.2 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.baq.1.7 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.baw.1.6 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.byl.1.3 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.byr.1.2 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.bzj.1.7 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.bzp.1.6 | $264$ | $2$ | $2$ | $1$ |