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: | $\begin{bmatrix}3&232\\244&165\end{bmatrix}$, $\begin{bmatrix}25&188\\132&113\end{bmatrix}$, $\begin{bmatrix}173&166\\158&93\end{bmatrix}$, $\begin{bmatrix}191&148\\92&117\end{bmatrix}$, $\begin{bmatrix}213&254\\148&263\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.3.fi.2 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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
3.8.0-3.a.1.1 | $3$ | $24$ | $24$ | $0$ | $0$ |
88.24.0-88.a.1.7 | $88$ | $8$ | $8$ | $0$ | $?$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.96.2-12.a.2.8 | $12$ | $2$ | $2$ | $2$ | $0$ |
264.96.0-264.o.2.32 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.96.0-264.o.2.63 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.96.1-264.dg.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.dg.1.34 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.2-12.a.2.1 | $264$ | $2$ | $2$ | $2$ | $?$ |
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.2.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.od.3.12 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.od.4.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.on.3.23 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.on.4.24 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.op.3.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.op.4.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pl.1.12 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pl.4.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.1.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.2.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pz.2.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pz.4.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.3.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.qb.4.16 | $264$ | $2$ | $2$ | $5$ |