Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12L3 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}15&214\\208&177\end{bmatrix}$, $\begin{bmatrix}57&130\\76&213\end{bmatrix}$, $\begin{bmatrix}119&0\\74&229\end{bmatrix}$, $\begin{bmatrix}125&24\\86&145\end{bmatrix}$, $\begin{bmatrix}221&252\\56&127\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.3.fi.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $5068800$ |
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 |
---|---|---|---|---|---|
12.96.2-12.a.1.8 | $12$ | $2$ | $2$ | $2$ | $0$ |
264.96.0-264.o.1.8 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.96.0-264.o.1.23 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.96.1-264.dg.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.dg.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.2-12.a.1.3 | $264$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.384.5-264.oc.1.8 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.od.1.8 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.od.2.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.on.1.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.on.2.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.op.1.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.op.2.6 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pl.2.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pl.3.13 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.3.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.4.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pz.1.13 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pz.3.11 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.1.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.2.14 | $264$ | $2$ | $2$ | $5$ |