Invariants
Level: | $232$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-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: | $\begin{bmatrix}55&132\\56&49\end{bmatrix}$, $\begin{bmatrix}71&204\\160&211\end{bmatrix}$, $\begin{bmatrix}95&108\\36&59\end{bmatrix}$, $\begin{bmatrix}103&192\\20&179\end{bmatrix}$, $\begin{bmatrix}185&132\\96&85\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 232.192.3-232.be.1.1, 232.192.3-232.be.1.2, 232.192.3-232.be.1.3, 232.192.3-232.be.1.4, 232.192.3-232.be.1.5, 232.192.3-232.be.1.6, 232.192.3-232.be.1.7, 232.192.3-232.be.1.8, 232.192.3-232.be.1.9, 232.192.3-232.be.1.10, 232.192.3-232.be.1.11, 232.192.3-232.be.1.12 |
Cyclic 232-isogeny field degree: | $60$ |
Cyclic 232-torsion field degree: | $3360$ |
Full 232-torsion field degree: | $10913280$ |
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 |
---|---|---|---|---|---|
8.48.0.c.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
232.48.1.n.1 | $232$ | $2$ | $2$ | $1$ | $?$ |
232.48.2.a.1 | $232$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
232.192.5.z.1 | $232$ | $2$ | $2$ | $5$ |
232.192.5.z.2 | $232$ | $2$ | $2$ | $5$ |
232.192.5.bb.3 | $232$ | $2$ | $2$ | $5$ |
232.192.5.bb.4 | $232$ | $2$ | $2$ | $5$ |