Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | 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 | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | 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: | 24V3 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}75&254\\56&129\end{bmatrix}$, $\begin{bmatrix}105&113\\224&237\end{bmatrix}$, $\begin{bmatrix}201&152\\92&159\end{bmatrix}$, $\begin{bmatrix}203&0\\20&223\end{bmatrix}$, $\begin{bmatrix}245&43\\180&115\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.96.3.mj.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $24$ |
| Cyclic 264-torsion field degree: | $960$ |
| 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 |
|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $48$ | $24$ | $0$ | $0$ |
| 88.48.0-88.bn.1.1 | $88$ | $4$ | $4$ | $0$ | $?$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 88.48.0-88.bn.1.1 | $88$ | $4$ | $4$ | $0$ | $?$ |
| 264.96.1-132.k.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.1-132.k.1.21 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.1-24.ix.1.11 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.1-264.zs.1.21 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.1-264.zs.1.42 | $264$ | $2$ | $2$ | $1$ | $?$ |
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.baq.1.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.baq.2.3 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.baq.3.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.baq.4.3 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bau.1.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bau.2.2 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bau.3.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bau.4.2 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bhk.1.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bhk.2.2 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bhk.3.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bhk.4.2 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bho.1.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bho.2.3 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bho.3.1 | $264$ | $2$ | $2$ | $5$ |
| 264.384.5-264.bho.4.3 | $264$ | $2$ | $2$ | $5$ |