Invariants
| Level: | $152$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $1^{2}\cdot2\cdot8$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8C0 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}20&63\\105&66\end{bmatrix}$, $\begin{bmatrix}24&67\\67&56\end{bmatrix}$, $\begin{bmatrix}129&8\\142&99\end{bmatrix}$, $\begin{bmatrix}130&59\\71&126\end{bmatrix}$, $\begin{bmatrix}132&117\\85&100\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 8.12.0.n.1 for the level structure with $-I$) |
| Cyclic 152-isogeny field degree: | $20$ |
| Cyclic 152-torsion field degree: | $1440$ |
| 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 5199 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 12 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{x^{12}(x^{4}-16x^{2}y^{2}+16y^{4})^{3}}{y^{8}x^{14}(x-4y)(x+4y)}$ |
Modular covers
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.i.1.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.k.1.3 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.q.1.5 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.r.1.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.1.7 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.2.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.2.7 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.1.7 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.2.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.2.7 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bf.1.8 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bh.1.11 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bj.1.8 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bl.1.11 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.1.16 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.2.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.2.15 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.1.15 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.2.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.2.16 | $152$ | $2$ | $2$ | $0$ |
| 152.480.17-152.bl.1.15 | $152$ | $20$ | $20$ | $17$ |
| 304.48.0-16.e.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.e.1.16 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.e.2.2 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.e.2.15 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.1.32 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.2.3 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.2.30 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.1.16 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.2.3 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.2.14 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.1.3 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.1.30 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.2.32 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.g.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.g.1.16 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.g.1.3 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.g.1.30 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.h.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.h.1.16 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.h.1.5 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.h.1.28 | $304$ | $2$ | $2$ | $0$ |
| 304.48.1-16.a.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-16.a.1.16 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.a.1.5 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.a.1.28 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-16.b.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-16.b.1.16 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.b.1.3 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.b.1.30 | $304$ | $2$ | $2$ | $1$ |