Invariants
| Level: | $141$ | $\SL_2$-level: | $3$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $3^{4}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | 3D0 |
Level structure
| $\GL_2(\Z/141\Z)$-generators: | $\begin{bmatrix}38&39\\72&44\end{bmatrix}$, $\begin{bmatrix}72&35\\59&33\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 3.12.0.a.1 for the level structure with $-I$) |
| Cyclic 141-isogeny field degree: | $48$ |
| Cyclic 141-torsion field degree: | $4416$ |
| Full 141-torsion field degree: | $9547392$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 1550 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 12 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{x^{15}(x+6y)^{3}(x^{2}-6xy+36y^{2})^{3}}{y^{3}x^{12}(x-3y)^{3}(x^{2}+3xy+9y^{2})^{3}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 141.8.0-3.a.1.1 | $141$ | $3$ | $3$ | $0$ | $?$ |
| 141.8.0-3.a.1.2 | $141$ | $3$ | $3$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 282.48.1-6.a.1.1 | $282$ | $2$ | $2$ | $1$ |
| 282.48.1-6.b.1.1 | $282$ | $2$ | $2$ | $1$ |
| 282.48.1-282.b.1.2 | $282$ | $2$ | $2$ | $1$ |
| 282.48.1-282.c.1.2 | $282$ | $2$ | $2$ | $1$ |
| 282.72.0-6.a.1.1 | $282$ | $3$ | $3$ | $0$ |