Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}35&72\\242&223\end{bmatrix}$, $\begin{bmatrix}43&252\\172&35\end{bmatrix}$, $\begin{bmatrix}71&248\\19&213\end{bmatrix}$, $\begin{bmatrix}193&216\\202&257\end{bmatrix}$, $\begin{bmatrix}217&56\\187&39\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.24.0.bg.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
Full 264-torsion field degree: | $20275200$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
---|---|---|---|---|---|
8.24.0-4.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
264.24.0-4.d.1.1 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.24.0-264.z.1.1 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.24.0-264.z.1.9 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.24.0-264.z.1.24 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.24.0-264.z.1.32 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.96.1-264.lg.1.5 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.lh.1.5 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.li.1.8 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.lj.1.8 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.lk.1.5 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.ll.1.5 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.lm.1.8 | $264$ | $2$ | $2$ | $1$ |
264.96.1-264.ln.1.8 | $264$ | $2$ | $2$ | $1$ |
264.144.4-264.fx.1.26 | $264$ | $3$ | $3$ | $4$ |
264.192.3-264.hl.1.33 | $264$ | $4$ | $4$ | $3$ |