Invariants
Level: | $152$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
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: | 8O0 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}23&92\\54&95\end{bmatrix}$, $\begin{bmatrix}53&0\\144&99\end{bmatrix}$, $\begin{bmatrix}87&140\\52&39\end{bmatrix}$, $\begin{bmatrix}95&124\\88&117\end{bmatrix}$, $\begin{bmatrix}117&76\\64&67\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 152.96.0-152.p.2.1, 152.96.0-152.p.2.2, 152.96.0-152.p.2.3, 152.96.0-152.p.2.4, 152.96.0-152.p.2.5, 152.96.0-152.p.2.6, 152.96.0-152.p.2.7, 152.96.0-152.p.2.8, 152.96.0-152.p.2.9, 152.96.0-152.p.2.10, 152.96.0-152.p.2.11, 152.96.0-152.p.2.12, 152.96.0-152.p.2.13, 152.96.0-152.p.2.14, 152.96.0-152.p.2.15, 152.96.0-152.p.2.16 |
Cyclic 152-isogeny field degree: | $40$ |
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.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
152.24.0.i.2 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.24.0.l.1 | $152$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
152.96.1.a.1 | $152$ | $2$ | $2$ | $1$ |
152.96.1.d.1 | $152$ | $2$ | $2$ | $1$ |
152.96.1.r.2 | $152$ | $2$ | $2$ | $1$ |
152.96.1.u.2 | $152$ | $2$ | $2$ | $1$ |
152.96.1.ba.2 | $152$ | $2$ | $2$ | $1$ |
152.96.1.bb.2 | $152$ | $2$ | $2$ | $1$ |
152.96.1.be.1 | $152$ | $2$ | $2$ | $1$ |
152.96.1.bf.1 | $152$ | $2$ | $2$ | $1$ |