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: | $\begin{bmatrix}89&144\\88&135\end{bmatrix}$, $\begin{bmatrix}99&130\\0&1\end{bmatrix}$, $\begin{bmatrix}109&114\\88&51\end{bmatrix}$, $\begin{bmatrix}127&150\\84&95\end{bmatrix}$, $\begin{bmatrix}145&52\\8&21\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 152.96.1-152.bc.2.1, 152.96.1-152.bc.2.2, 152.96.1-152.bc.2.3, 152.96.1-152.bc.2.4, 152.96.1-152.bc.2.5, 152.96.1-152.bc.2.6, 152.96.1-152.bc.2.7, 152.96.1-152.bc.2.8, 152.96.1-152.bc.2.9, 152.96.1-152.bc.2.10, 152.96.1-152.bc.2.11, 152.96.1-152.bc.2.12, 152.96.1-152.bc.2.13, 152.96.1-152.bc.2.14, 152.96.1-152.bc.2.15, 152.96.1-152.bc.2.16 |
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 real points and $\Q_p$ points for $p$ not dividing the level, but no known 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.h.2 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
152.24.1.c.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.b.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.h.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bb.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bd.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bt.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.bv.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.ca.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.96.1.cb.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |