Invariants
| Level: | $132$ | $\SL_2$-level: | $12$ | ||||
| Index: | $24$ | $\PSL_2$-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 | $1^{2}\cdot3^{2}\cdot4\cdot12$ | 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: | 12E0 |
Level structure
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 |
|---|---|---|---|---|---|
| $X_0(6)$ | $6$ | $2$ | $2$ | $0$ | $0$ |
| 132.6.0.b.1 | $132$ | $4$ | $4$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 132.48.1.c.1 | $132$ | $2$ | $2$ | $1$ |
| 132.48.1.f.1 | $132$ | $2$ | $2$ | $1$ |
| 132.48.1.z.1 | $132$ | $2$ | $2$ | $1$ |
| 132.48.1.ba.1 | $132$ | $2$ | $2$ | $1$ |
| 132.48.1.bh.1 | $132$ | $2$ | $2$ | $1$ |
| 132.48.1.bi.1 | $132$ | $2$ | $2$ | $1$ |
| 132.48.1.bt.1 | $132$ | $2$ | $2$ | $1$ |
| 132.48.1.bu.1 | $132$ | $2$ | $2$ | $1$ |
| 132.72.1.p.1 | $132$ | $3$ | $3$ | $1$ |
| 132.288.19.cc.1 | $132$ | $12$ | $12$ | $19$ |
| 264.48.1.gh.1 | $264$ | $2$ | $2$ | $1$ |
| 264.48.1.ka.1 | $264$ | $2$ | $2$ | $1$ |
| 264.48.1.bky.1 | $264$ | $2$ | $2$ | $1$ |
| 264.48.1.blb.1 | $264$ | $2$ | $2$ | $1$ |
| 264.48.1.bym.1 | $264$ | $2$ | $2$ | $1$ |
| 264.48.1.byp.1 | $264$ | $2$ | $2$ | $1$ |
| 264.48.1.bzw.1 | $264$ | $2$ | $2$ | $1$ |
| 264.48.1.bzz.1 | $264$ | $2$ | $2$ | $1$ |