Invariants
Level: | $152$ | $\SL_2$-level: | $4$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 4G0 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}5&118\\64&121\end{bmatrix}$, $\begin{bmatrix}85&52\\66&149\end{bmatrix}$, $\begin{bmatrix}129&16\\28&147\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 152.24.0.g.1 for the level structure with $-I$) |
Cyclic 152-isogeny field degree: | $80$ |
Cyclic 152-torsion field degree: | $2880$ |
Full 152-torsion field degree: | $3939840$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.24.0-8.b.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
152.24.0-8.b.1.3 | $152$ | $2$ | $2$ | $0$ | $?$ |
76.24.0-76.b.1.2 | $76$ | $2$ | $2$ | $0$ | $?$ |
152.24.0-76.b.1.3 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.24.0-152.a.1.2 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.24.0-152.a.1.6 | $152$ | $2$ | $2$ | $0$ | $?$ |