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 | $2^{2}\cdot4^{3}\cdot8$ | 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: | 8J0 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}41&104\\78&95\end{bmatrix}$, $\begin{bmatrix}69&72\\60&81\end{bmatrix}$, $\begin{bmatrix}77&24\\140&133\end{bmatrix}$, $\begin{bmatrix}111&44\\34&53\end{bmatrix}$, $\begin{bmatrix}129&148\\104&55\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 152.24.0.i.2 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.1.9 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 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.b.2.22 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.c.1.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.e.1.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.f.1.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.h.1.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.j.2.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.l.1.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.n.1.15 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.p.2.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.r.2.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.t.2.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.v.1.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.x.2.14 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.y.1.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.ba.1.16 | $152$ | $2$ | $2$ | $0$ |
| 152.96.0-152.bb.2.12 | $152$ | $2$ | $2$ | $0$ |
| 152.96.1-152.q.1.4 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.s.1.12 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.x.1.14 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.y.1.12 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bd.1.14 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bf.2.4 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bh.1.14 | $152$ | $2$ | $2$ | $1$ |
| 152.96.1-152.bj.1.15 | $152$ | $2$ | $2$ | $1$ |