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: | $\begin{bmatrix}99&232\\196&87\end{bmatrix}$, $\begin{bmatrix}151&104\\36&89\end{bmatrix}$, $\begin{bmatrix}155&66\\50&181\end{bmatrix}$, $\begin{bmatrix}157&140\\138&263\end{bmatrix}$, $\begin{bmatrix}239&222\\44&181\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.96.3.eo.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.1.8 | $88$ | $8$ | $8$ | $0$ | $?$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.96.0-24.o.2.31 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 132.96.2-132.a.1.14 | $132$ | $2$ | $2$ | $2$ | $?$ |
| 264.96.0-24.o.2.27 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.96.1-264.dg.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.1-264.dg.1.28 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.2-132.a.1.9 | $264$ | $2$ | $2$ | $2$ | $?$ |
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.iq.2.16 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ir.3.16 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ir.4.15 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jb.3.15 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jb.4.24 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jd.3.15 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jd.4.14 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jz.2.16 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jz.4.14 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kb.3.16 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kb.4.16 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kn.1.14 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kn.3.12 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kp.1.8 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kp.3.16 | $264$ | $2$ | $2$ | $5$ |