Invariants
| Level: | $152$ | $\SL_2$-level: | $4$ | ||||
| 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 | $2^{2}\cdot4^{2}$ | 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: | 4E0 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}11&40\\142&75\end{bmatrix}$, $\begin{bmatrix}97&146\\56&149\end{bmatrix}$, $\begin{bmatrix}103&96\\80&5\end{bmatrix}$, $\begin{bmatrix}125&122\\44&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 8.12.0.b.1 for the level structure with $-I$) |
| Cyclic 152-isogeny field degree: | $80$ |
| Cyclic 152-torsion field degree: | $5760$ |
| Full 152-torsion field degree: | $7879680$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 624 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 12 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle 2^2\,\frac{x^{12}(64x^{4}+8x^{2}y^{2}+y^{4})^{3}}{y^{4}x^{16}(8x^{2}+y^{2})^{2}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 76.12.0-2.a.1.1 | $76$ | $2$ | $2$ | $0$ | $?$ |
| 152.12.0-2.a.1.2 | $152$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 152.48.0-8.b.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.c.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.c.1.8 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.f.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.f.1.3 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.g.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.g.1.3 | $152$ | $2$ | $2$ | $0$ |
| 152.480.17-152.b.1.15 | $152$ | $20$ | $20$ | $17$ |