Invariants
Level: | $232$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}23&208\\44&113\end{bmatrix}$, $\begin{bmatrix}31&132\\100&109\end{bmatrix}$, $\begin{bmatrix}95&128\\116&211\end{bmatrix}$, $\begin{bmatrix}135&104\\92&199\end{bmatrix}$, $\begin{bmatrix}183&80\\8&1\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 232.192.1-232.x.1.1, 232.192.1-232.x.1.2, 232.192.1-232.x.1.3, 232.192.1-232.x.1.4, 232.192.1-232.x.1.5, 232.192.1-232.x.1.6, 232.192.1-232.x.1.7, 232.192.1-232.x.1.8, 232.192.1-232.x.1.9, 232.192.1-232.x.1.10, 232.192.1-232.x.1.11, 232.192.1-232.x.1.12 |
Cyclic 232-isogeny field degree: | $60$ |
Cyclic 232-torsion field degree: | $3360$ |
Full 232-torsion field degree: | $10913280$ |
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 |
---|---|---|---|---|---|---|
8.48.0.c.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
232.48.0.b.2 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.0.w.1 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.0.x.1 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.1.o.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.48.1.be.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.48.1.bf.2 | $232$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
232.192.5.x.1 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |
232.192.5.y.2 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |
232.192.5.ba.2 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |
232.192.5.bb.3 | $232$ | $2$ | $2$ | $5$ | $?$ | not computed |