Invariants
| Level: | $152$ | $\SL_2$-level: | $8$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| 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: | 8N0 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}13&48\\20&31\end{bmatrix}$, $\begin{bmatrix}19&42\\36&85\end{bmatrix}$, $\begin{bmatrix}43&68\\4&15\end{bmatrix}$, $\begin{bmatrix}151&48\\100&39\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 152.48.0.n.2 for the level structure with $-I$) |
| Cyclic 152-isogeny field degree: | $40$ |
| Cyclic 152-torsion field degree: | $2880$ |
| Full 152-torsion field degree: | $1969920$ |
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 |
|---|---|---|---|---|---|
| 8.48.0-8.e.1.15 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 152.48.0-8.e.1.4 | $152$ | $2$ | $2$ | $0$ | $?$ |
| 152.48.0-152.e.1.8 | $152$ | $2$ | $2$ | $0$ | $?$ |
| 152.48.0-152.e.1.20 | $152$ | $2$ | $2$ | $0$ | $?$ |
| 152.48.0-152.i.1.16 | $152$ | $2$ | $2$ | $0$ | $?$ |
| 152.48.0-152.i.1.28 | $152$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 152.192.1-152.u.1.7 | $152$ | $2$ | $2$ | $1$ |
| 152.192.1-152.z.2.3 | $152$ | $2$ | $2$ | $1$ |
| 152.192.1-152.bm.1.2 | $152$ | $2$ | $2$ | $1$ |
| 152.192.1-152.bo.1.7 | $152$ | $2$ | $2$ | $1$ |
| 152.192.1-152.bx.1.8 | $152$ | $2$ | $2$ | $1$ |
| 152.192.1-152.bz.2.4 | $152$ | $2$ | $2$ | $1$ |
| 152.192.1-152.cg.1.4 | $152$ | $2$ | $2$ | $1$ |
| 152.192.1-152.ch.1.8 | $152$ | $2$ | $2$ | $1$ |