Invariants
| Level: | $152$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| 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: | 4G0 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}5&124\\72&115\end{bmatrix}$, $\begin{bmatrix}43&54\\28&57\end{bmatrix}$, $\begin{bmatrix}55&16\\84&17\end{bmatrix}$, $\begin{bmatrix}101&34\\36&3\end{bmatrix}$, $\begin{bmatrix}135&104\\8&145\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 76.24.0.c.1 for the level structure with $-I$) |
| Cyclic 152-isogeny field degree: | $40$ |
| Cyclic 152-torsion field degree: | $2880$ |
| Full 152-torsion field degree: | $3939840$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-4.b.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 152.24.0-4.b.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 |
|---|---|---|---|---|
| 152.96.0-152.g.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.g.1.7 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.g.2.4 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.g.2.5 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.h.1.11 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.h.1.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.h.2.7 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.h.2.12 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.i.1.11 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.i.1.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.i.2.4 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.i.2.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.j.1.2 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.j.1.7 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.j.2.4 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.j.2.5 | $152$ | $2$ | $2$ | $0$ |
| 152.96.1-152.p.1.2 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.p.1.15 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.u.1.8 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.u.1.9 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bs.1.8 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bs.1.9 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bu.1.4 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bu.1.13 | $152$ | $2$ | $2$ | $1$ |