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: | $12$ (of which $2$ are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $1^{2}\cdot2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12L3 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}67&42\\198&241\end{bmatrix}$, $\begin{bmatrix}77&256\\194&87\end{bmatrix}$, $\begin{bmatrix}101&228\\56&43\end{bmatrix}$, $\begin{bmatrix}147&50\\100&173\end{bmatrix}$, $\begin{bmatrix}197&76\\164&33\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.96.3.em.2 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $48$ |
| Cyclic 264-torsion field degree: | $1920$ |
| Full 264-torsion field degree: | $5068800$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal 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.1.6 | $88$ | $8$ | $8$ | $0$ | $?$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.96.0-12.a.2.15 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 264.96.0-12.a.2.6 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.96.1-264.dg.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.1-264.dg.1.26 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.2-264.b.2.2 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.96.2-264.b.2.27 | $264$ | $2$ | $2$ | $2$ | $?$ |
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.in.1.9 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ip.2.13 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ip.4.13 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ix.1.9 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ix.2.17 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ja.2.13 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.ja.4.13 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jv.2.15 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jv.4.15 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jy.2.13 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.jy.4.11 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kj.3.15 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.kj.4.15 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.km.2.7 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.km.3.11 | $264$ | $2$ | $2$ | $5$ |