Invariants
Level: | $252$ | $\SL_2$-level: | $36$ | Newform level: | $1$ | ||
Index: | $216$ | $\PSL_2$-index: | $108$ | ||||
Genus: | $2 = 1 + \frac{ 108 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $1^{3}\cdot2^{3}\cdot3^{2}\cdot6^{2}\cdot9^{3}\cdot18^{3}$ | Cusp orbits | $2^{2}\cdot3^{4}$ | ||
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: | 18Q2 |
Level structure
$\GL_2(\Z/252\Z)$-generators: | $\begin{bmatrix}94&211\\195&146\end{bmatrix}$, $\begin{bmatrix}191&26\\240&49\end{bmatrix}$, $\begin{bmatrix}192&121\\131&164\end{bmatrix}$, $\begin{bmatrix}215&54\\190&79\end{bmatrix}$, $\begin{bmatrix}222&131\\11&234\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 126.108.2.f.2 for the level structure with $-I$) |
Cyclic 252-isogeny field degree: | $16$ |
Cyclic 252-torsion field degree: | $1152$ |
Full 252-torsion field degree: | $3483648$ |
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 |
---|---|---|---|---|---|
36.72.0-18.a.1.12 | $36$ | $3$ | $3$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.