Invariants
Level: | $232$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}41&12\\172&81\end{bmatrix}$, $\begin{bmatrix}43&76\\88&73\end{bmatrix}$, $\begin{bmatrix}81&48\\4&95\end{bmatrix}$, $\begin{bmatrix}121&40\\28&197\end{bmatrix}$, $\begin{bmatrix}179&156\\76&97\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 232.48.1.n.2 for the level structure with $-I$) |
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 is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-4.b.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
232.48.0-4.b.1.4 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.0-232.l.1.1 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.0-232.l.1.17 | $232$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
232.48.1-232.d.1.6 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.48.1-232.d.1.8 | $232$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
232.192.1-232.a.1.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.1-232.a.2.1 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.1-232.g.1.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.1-232.g.2.1 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.1-232.r.1.1 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.1-232.r.2.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.1-232.w.1.1 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.1-232.w.2.2 | $232$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
232.192.3-232.r.1.4 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |
232.192.3-232.r.2.4 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |
232.192.3-232.t.1.4 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |
232.192.3-232.t.2.6 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |
232.192.3-232.w.1.2 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |
232.192.3-232.w.2.4 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |
232.192.3-232.y.1.2 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |
232.192.3-232.y.2.8 | $232$ | $2$ | $2$ | $3$ | $?$ | not computed |