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: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/228\Z)$-generators: | $\begin{bmatrix}13&24\\190&83\end{bmatrix}$, $\begin{bmatrix}31&180\\0&37\end{bmatrix}$, $\begin{bmatrix}73&222\\224&35\end{bmatrix}$, $\begin{bmatrix}169&120\\202&133\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 228.96.1.h.2 for the level structure with $-I$) |
Cyclic 228-isogeny field degree: | $40$ |
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 is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.96.0-12.a.1.15 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
228.96.0-12.a.1.13 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.96.0-228.a.1.8 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.96.0-228.a.1.15 | $228$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
228.96.1-228.d.1.7 | $228$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
228.96.1-228.d.1.18 | $228$ | $2$ | $2$ | $1$ | $?$ | 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.j.1.6 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.k.1.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.m.4.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.n.4.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.t.2.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.u.2.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.w.1.6 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |
228.384.5-228.x.3.4 | $228$ | $2$ | $2$ | $5$ | $?$ | not computed |