Invariants
Level: | $152$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}13&14\\32&59\end{bmatrix}$, $\begin{bmatrix}51&140\\80&21\end{bmatrix}$, $\begin{bmatrix}75&110\\72&29\end{bmatrix}$, $\begin{bmatrix}113&24\\28&57\end{bmatrix}$, $\begin{bmatrix}123&102\\52&145\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 152.96.1-152.bh.1.1, 152.96.1-152.bh.1.2, 152.96.1-152.bh.1.3, 152.96.1-152.bh.1.4, 152.96.1-152.bh.1.5, 152.96.1-152.bh.1.6, 152.96.1-152.bh.1.7, 152.96.1-152.bh.1.8, 152.96.1-152.bh.1.9, 152.96.1-152.bh.1.10, 152.96.1-152.bh.1.11, 152.96.1-152.bh.1.12, 152.96.1-152.bh.1.13, 152.96.1-152.bh.1.14, 152.96.1-152.bh.1.15, 152.96.1-152.bh.1.16 |
Cyclic 152-isogeny field degree: | $40$ |
Cyclic 152-torsion field degree: | $2880$ |
Full 152-torsion field degree: | $3939840$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
8.24.0.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
152.24.0.i.2 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
152.24.1.d.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
152.96.1.a.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.r.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bj.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bn.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bs.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bw.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.ce.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.cg.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |