Invariants
Level: | $232$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}111&208\\52&7\end{bmatrix}$, $\begin{bmatrix}141&160\\142&99\end{bmatrix}$, $\begin{bmatrix}167&12\\54&79\end{bmatrix}$, $\begin{bmatrix}181&196\\86&9\end{bmatrix}$, $\begin{bmatrix}191&144\\6&63\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 232.96.0-232.v.1.1, 232.96.0-232.v.1.2, 232.96.0-232.v.1.3, 232.96.0-232.v.1.4, 232.96.0-232.v.1.5, 232.96.0-232.v.1.6, 232.96.0-232.v.1.7, 232.96.0-232.v.1.8, 232.96.0-232.v.1.9, 232.96.0-232.v.1.10, 232.96.0-232.v.1.11, 232.96.0-232.v.1.12, 232.96.0-232.v.1.13, 232.96.0-232.v.1.14, 232.96.0-232.v.1.15, 232.96.0-232.v.1.16 |
Cyclic 232-isogeny field degree: | $60$ |
Cyclic 232-torsion field degree: | $6720$ |
Full 232-torsion field degree: | $21826560$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
---|---|---|---|---|---|
8.24.0.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
232.24.0.i.1 | $232$ | $2$ | $2$ | $0$ | $?$ |
232.24.0.m.1 | $232$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
232.96.1.b.1 | $232$ | $2$ | $2$ | $1$ |
232.96.1.c.1 | $232$ | $2$ | $2$ | $1$ |
232.96.1.s.1 | $232$ | $2$ | $2$ | $1$ |
232.96.1.t.1 | $232$ | $2$ | $2$ | $1$ |
232.96.1.bi.1 | $232$ | $2$ | $2$ | $1$ |
232.96.1.bj.1 | $232$ | $2$ | $2$ | $1$ |
232.96.1.bm.1 | $232$ | $2$ | $2$ | $1$ |
232.96.1.bn.1 | $232$ | $2$ | $2$ | $1$ |