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 | $2^{4}\cdot4^{2}\cdot8^{4}$ | 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: | 8O0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}49&196\\168&259\end{bmatrix}$, $\begin{bmatrix}53&96\\24&199\end{bmatrix}$, $\begin{bmatrix}63&196\\218&189\end{bmatrix}$, $\begin{bmatrix}103&96\\0&239\end{bmatrix}$, $\begin{bmatrix}221&260\\156&185\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.0.bx.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
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 |
---|---|---|---|---|---|
24.48.0-8.d.2.9 | $24$ | $2$ | $2$ | $0$ | $0$ |
88.48.0-8.d.2.12 | $88$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.u.1.49 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.u.1.56 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.y.1.15 | $264$ | $2$ | $2$ | $0$ | $?$ |
264.48.0-264.y.1.27 | $264$ | $2$ | $2$ | $0$ | $?$ |
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.b.2.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.c.2.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ca.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.cd.2.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ei.1.10 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.ej.2.8 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.eq.2.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.er.2.6 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.fq.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.fr.2.14 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.fy.2.8 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.fz.2.12 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.hm.2.8 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.hn.2.4 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.hu.1.11 | $264$ | $2$ | $2$ | $1$ |
264.192.1-264.hv.2.12 | $264$ | $2$ | $2$ | $1$ |
264.288.8-264.mh.1.62 | $264$ | $3$ | $3$ | $8$ |
264.384.7-264.gs.2.54 | $264$ | $4$ | $4$ | $7$ |