Invariants
Level: | $152$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 24$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B1 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}5&49\\38&117\end{bmatrix}$, $\begin{bmatrix}41&67\\18&67\end{bmatrix}$, $\begin{bmatrix}115&150\\88&135\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 152-isogeny field degree: | $80$ |
Cyclic 152-torsion field degree: | $5760$ |
Full 152-torsion field degree: | $7879680$ |
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 |
---|---|---|---|---|---|---|
8.12.1.a.1 | $8$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
76.12.0.i.1 | $76$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
152.12.0.bv.1 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |