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 | $2^{2}\cdot4^{2}$ | ||
| 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: | 12K3 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}11&219\\52&169\end{bmatrix}$, $\begin{bmatrix}135&103\\46&213\end{bmatrix}$, $\begin{bmatrix}191&5\\30&193\end{bmatrix}$, $\begin{bmatrix}191&146\\232&123\end{bmatrix}$, $\begin{bmatrix}227&77\\66&1\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.96.3.rn.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 |
|---|---|---|---|---|---|
| 12.96.1-12.o.1.3 | $12$ | $2$ | $2$ | $1$ | $0$ |
| 264.96.1-12.o.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.2-264.m.1.42 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.96.2-264.m.1.49 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.96.2-264.o.1.42 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.96.2-264.o.1.49 | $264$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.384.9-264.bjz.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.bkf.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.bkn.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.bkx.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.bxa.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.bxc.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.bzk.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.bzq.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cgu.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cha.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cji.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cjk.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cqy.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cri.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.crq.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.crw.1.10 | $264$ | $2$ | $2$ | $9$ |