Invariants
Level: | $232$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G0 |
Level structure
$\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}5&116\\82&1\end{bmatrix}$, $\begin{bmatrix}19&84\\161&217\end{bmatrix}$, $\begin{bmatrix}125&0\\90&13\end{bmatrix}$, $\begin{bmatrix}149&112\\215&115\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 232.24.0.v.1 for the level structure with $-I$) |
Cyclic 232-isogeny field degree: | $60$ |
Cyclic 232-torsion field degree: | $6720$ |
Full 232-torsion field degree: | $21826560$ |
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 |
---|---|---|---|---|---|
8.24.0-4.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
116.24.0-4.d.1.1 | $116$ | $2$ | $2$ | $0$ | $?$ |
232.24.0-232.y.1.1 | $232$ | $2$ | $2$ | $0$ | $?$ |
232.24.0-232.y.1.5 | $232$ | $2$ | $2$ | $0$ | $?$ |
232.24.0-232.y.1.12 | $232$ | $2$ | $2$ | $0$ | $?$ |
232.24.0-232.y.1.16 | $232$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
232.96.1-232.dg.1.3 | $232$ | $2$ | $2$ | $1$ |
232.96.1-232.dh.1.4 | $232$ | $2$ | $2$ | $1$ |
232.96.1-232.di.1.4 | $232$ | $2$ | $2$ | $1$ |
232.96.1-232.dj.1.4 | $232$ | $2$ | $2$ | $1$ |