Invariants
Level: | $228$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-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 | $2^{6}\cdot4$ | ||
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: | $\begin{bmatrix}11&54\\12&119\end{bmatrix}$, $\begin{bmatrix}37&120\\184&187\end{bmatrix}$, $\begin{bmatrix}49&60\\182&133\end{bmatrix}$, $\begin{bmatrix}97&204\\96&167\end{bmatrix}$, $\begin{bmatrix}145&102\\76&161\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 228.192.1-228.f.2.1, 228.192.1-228.f.2.2, 228.192.1-228.f.2.3, 228.192.1-228.f.2.4, 228.192.1-228.f.2.5, 228.192.1-228.f.2.6, 228.192.1-228.f.2.7, 228.192.1-228.f.2.8, 228.192.1-228.f.2.9, 228.192.1-228.f.2.10, 228.192.1-228.f.2.11, 228.192.1-228.f.2.12, 228.192.1-228.f.2.13, 228.192.1-228.f.2.14, 228.192.1-228.f.2.15, 228.192.1-228.f.2.16 |
Cyclic 228-isogeny field degree: | $40$ |
Cyclic 228-torsion field degree: | $2880$ |
Full 228-torsion field degree: | $5909760$ |
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
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0.a.2 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
228.48.0.a.1 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.48.1.b.1 | $228$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
228.192.5.g.1 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.192.5.h.1 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.192.5.m.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.192.5.o.2 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.192.5.q.2 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.192.5.r.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.192.5.w.3 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.192.5.y.3 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.288.9.d.1 | $228$ | $3$ | $3$ | $9$ | $?$ | not computed |