Invariants
Level: | $232$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $8^{12}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B3 |
Level structure
$\GL_2(\Z/232\Z)$-generators: | $\begin{bmatrix}49&68\\116&141\end{bmatrix}$, $\begin{bmatrix}169&144\\108&53\end{bmatrix}$, $\begin{bmatrix}231&144\\28&159\end{bmatrix}$, $\begin{bmatrix}231&156\\0&181\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 232.96.3.be.1 for the level structure with $-I$) |
Cyclic 232-isogeny field degree: | $60$ |
Cyclic 232-torsion field degree: | $3360$ |
Full 232-torsion field degree: | $5456640$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.96.0-8.c.1.7 | $8$ | $2$ | $2$ | $0$ | $0$ |
232.96.0-8.c.1.6 | $232$ | $2$ | $2$ | $0$ | $?$ |
232.96.1-232.n.1.3 | $232$ | $2$ | $2$ | $1$ | $?$ |
232.96.1-232.n.1.10 | $232$ | $2$ | $2$ | $1$ | $?$ |
232.96.2-232.a.1.5 | $232$ | $2$ | $2$ | $2$ | $?$ |
232.96.2-232.a.1.11 | $232$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
232.384.5-232.z.1.4 | $232$ | $2$ | $2$ | $5$ |
232.384.5-232.z.1.7 | $232$ | $2$ | $2$ | $5$ |
232.384.5-232.z.2.3 | $232$ | $2$ | $2$ | $5$ |
232.384.5-232.z.2.5 | $232$ | $2$ | $2$ | $5$ |
232.384.5-232.bb.3.4 | $232$ | $2$ | $2$ | $5$ |
232.384.5-232.bb.3.6 | $232$ | $2$ | $2$ | $5$ |
232.384.5-232.bb.4.3 | $232$ | $2$ | $2$ | $5$ |
232.384.5-232.bb.4.5 | $232$ | $2$ | $2$ | $5$ |