Invariants
Level: | $228$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $36$ | $\PSL_2$-index: | $36$ | ||||
Genus: | $2 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $6^{2}\cdot12^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12B2 |
Level structure
$\GL_2(\Z/228\Z)$-generators: | $\begin{bmatrix}161&120\\154&91\end{bmatrix}$, $\begin{bmatrix}161&181\\148&169\end{bmatrix}$, $\begin{bmatrix}173&173\\158&219\end{bmatrix}$, $\begin{bmatrix}213&143\\40&153\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 228-isogeny field degree: | $160$ |
Cyclic 228-torsion field degree: | $11520$ |
Full 228-torsion field degree: | $15759360$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.18.1.f.1 | $12$ | $2$ | $2$ | $1$ | $0$ |
114.18.1.b.1 | $114$ | $2$ | $2$ | $1$ | $?$ |
228.12.0.o.1 | $228$ | $3$ | $3$ | $0$ | $?$ |
228.18.0.i.1 | $228$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
228.72.3.hw.1 | $228$ | $2$ | $2$ | $3$ |
228.72.3.hx.1 | $228$ | $2$ | $2$ | $3$ |
228.72.3.ie.1 | $228$ | $2$ | $2$ | $3$ |
228.72.3.if.1 | $228$ | $2$ | $2$ | $3$ |
228.72.3.ky.1 | $228$ | $2$ | $2$ | $3$ |
228.72.3.kz.1 | $228$ | $2$ | $2$ | $3$ |
228.72.3.lg.1 | $228$ | $2$ | $2$ | $3$ |
228.72.3.lh.1 | $228$ | $2$ | $2$ | $3$ |