Invariants
| Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $12^{6}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12A4 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}53&100\\82&225\end{bmatrix}$, $\begin{bmatrix}157&236\\26&215\end{bmatrix}$, $\begin{bmatrix}169&196\\42&245\end{bmatrix}$, $\begin{bmatrix}171&172\\140&141\end{bmatrix}$, $\begin{bmatrix}195&238\\202&61\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.72.4.k.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $192$ |
| Cyclic 264-torsion field degree: | $15360$ |
| Full 264-torsion field degree: | $6758400$ |
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 |
|---|---|---|---|---|---|
| 24.72.2-24.a.1.12 | $24$ | $2$ | $2$ | $2$ | $1$ |
| 132.72.2-132.d.1.12 | $132$ | $2$ | $2$ | $2$ | $?$ |
| 264.48.0-264.d.1.8 | $264$ | $3$ | $3$ | $0$ | $?$ |
| 264.72.2-24.a.1.7 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.72.2-132.d.1.15 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.72.2-264.d.1.7 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.72.2-264.d.1.29 | $264$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.288.7-264.fr.1.8 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.ft.1.10 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.gd.1.15 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.gf.1.6 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.kt.1.22 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.kv.1.16 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.lf.1.8 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.lh.1.16 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.pn.1.8 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.pp.1.11 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.pz.1.12 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.qb.1.5 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.uh.1.12 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.uj.1.14 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.ut.1.8 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.uv.1.16 | $264$ | $2$ | $2$ | $7$ |