Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
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: | 8N0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}23&184\\236&231\end{bmatrix}$, $\begin{bmatrix}125&246\\240&175\end{bmatrix}$, $\begin{bmatrix}207&110\\4&251\end{bmatrix}$, $\begin{bmatrix}229&244\\96&53\end{bmatrix}$, $\begin{bmatrix}257&20\\200&229\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.0.bj.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $10137600$ |
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 |
---|---|---|---|---|---|
24.48.0-24.i.2.5 | $24$ | $2$ | $2$ | $0$ | $0$ |
88.48.0-88.h.1.11 | $88$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.e.1.28 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.e.1.35 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-88.h.1.18 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-24.i.2.24 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.192.1-264.s.2.8 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.cw.2.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.em.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.eu.1.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ih.1.9 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ip.2.4 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.kc.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.kk.1.9 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.md.2.4 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ml.2.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ny.1.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.og.2.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.pf.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.pn.2.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.qa.2.2 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.qe.1.10 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.du.1.47 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.dk.2.41 | $264$ | $4$ | $4$ | $7$ |