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: | $\begin{bmatrix}24&27\\11&8\end{bmatrix}$, $\begin{bmatrix}25&72\\66&119\end{bmatrix}$, $\begin{bmatrix}85&150\\140&135\end{bmatrix}$, $\begin{bmatrix}126&121\\57&46\end{bmatrix}$, $\begin{bmatrix}148&81\\75&130\end{bmatrix}$ |
| 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.1.10 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.k.1.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.q.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.r.1.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.1.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.1.5 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.2.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.2.5 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.1.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.1.5 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.2.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.2.5 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bf.1.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bh.1.12 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bj.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bl.1.12 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.1.7 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.1.10 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.2.5 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.2.12 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.1.5 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.1.12 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.2.7 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.2.10 | $152$ | $2$ | $2$ | $0$ |
| 152.480.17-152.bl.1.8 | $152$ | $20$ | $20$ | $17$ |
| 304.48.0-16.e.1.7 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.e.1.10 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.e.2.8 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.e.2.9 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.1.13 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.1.20 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.2.9 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.2.24 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.1.4 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.1.13 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.2.2 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.2.15 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.1.9 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.1.24 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.2.13 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.2.20 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.g.1.7 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.g.1.10 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.g.1.15 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.g.1.18 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.h.1.7 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.h.1.10 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.h.1.15 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.h.1.18 | $304$ | $2$ | $2$ | $0$ |
| 304.48.1-16.a.1.7 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-16.a.1.10 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.a.1.15 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.a.1.18 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-16.b.1.7 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-16.b.1.10 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.b.1.15 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.b.1.18 | $304$ | $2$ | $2$ | $1$ |