Invariants
Level: | $228$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $2^{8}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/228\Z)$-generators: | $\begin{bmatrix}25&120\\182&131\end{bmatrix}$, $\begin{bmatrix}37&108\\158&13\end{bmatrix}$, $\begin{bmatrix}91&144\\172&41\end{bmatrix}$, $\begin{bmatrix}109&192\\122&41\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 228.96.1.b.4 for the level structure with $-I$) |
Cyclic 228-isogeny field degree: | $20$ |
Cyclic 228-torsion field degree: | $1440$ |
Full 228-torsion field degree: | $2954880$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
3.8.0-3.a.1.1 | $3$ | $24$ | $24$ | $0$ | $0$ | full Jacobian |
76.24.0-4.b.1.1 | $76$ | $8$ | $8$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.96.1-12.b.1.12 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
228.96.0-228.a.1.8 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.96.0-228.a.1.31 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.96.0-228.c.2.7 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.96.0-228.c.2.10 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.96.1-12.b.1.11 | $228$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
228.384.5-228.b.2.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.e.2.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.r.2.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.u.2.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |