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: | $\begin{bmatrix}7&32\\108&75\end{bmatrix}$, $\begin{bmatrix}7&114\\120&113\end{bmatrix}$, $\begin{bmatrix}30&21\\53&14\end{bmatrix}$, $\begin{bmatrix}108&43\\49&142\end{bmatrix}$, $\begin{bmatrix}124&105\\107&114\end{bmatrix}$ |
| 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 minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 76.12.0-4.c.1.1 | $76$ | $2$ | $2$ | $0$ | $?$ |
| 152.12.0-4.c.1.5 | $152$ | $2$ | $2$ | $0$ | $?$ |
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.i.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.k.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.q.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.r.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.1.7 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.ba.2.4 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.1.8 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-8.bb.2.3 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bf.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bh.1.3 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bj.1.9 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bl.1.1 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.1.9 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bu.2.13 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.1.9 | $152$ | $2$ | $2$ | $0$ |
| 152.48.0-152.bv.2.11 | $152$ | $2$ | $2$ | $0$ |
| 152.480.17-152.bl.1.35 | $152$ | $20$ | $20$ | $17$ |
| 304.48.0-16.e.1.3 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.e.2.12 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.1.17 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.e.2.25 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.1.6 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.f.2.7 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.1.17 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.f.2.21 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.g.1.3 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.g.1.27 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-16.h.1.3 | $304$ | $2$ | $2$ | $0$ |
| 304.48.0-304.h.1.21 | $304$ | $2$ | $2$ | $0$ |
| 304.48.1-16.a.1.14 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.a.1.12 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-16.b.1.14 | $304$ | $2$ | $2$ | $1$ |
| 304.48.1-304.b.1.6 | $304$ | $2$ | $2$ | $1$ |