Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | ||||
Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8$ | Cusp orbits | $1^{2}\cdot2$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8C0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}120&257\\61&208\end{bmatrix}$, $\begin{bmatrix}200&107\\131&48\end{bmatrix}$, $\begin{bmatrix}226&181\\69&10\end{bmatrix}$, $\begin{bmatrix}250&75\\45&256\end{bmatrix}$, $\begin{bmatrix}262&251\\213&164\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.12.0.y.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $40550400$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.12.0-4.c.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ |
264.12.0-4.c.1.1 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.48.0-264.x.1.17 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.z.1.16 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.bf.1.4 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.bh.1.10 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.bv.1.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.bw.1.13 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.by.1.5 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.cb.1.9 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.ck.1.13 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.cn.1.10 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.cp.1.9 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.cq.1.14 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.da.1.6 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dd.1.9 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dr.1.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.ds.1.15 | $264$ | $2$ | $2$ | $0$ |
264.72.2-264.cw.1.15 | $264$ | $3$ | $3$ | $2$ |
264.96.1-264.zu.1.26 | $264$ | $4$ | $4$ | $1$ |
264.288.9-264.ijy.1.25 | $264$ | $12$ | $12$ | $9$ |