Invariants
Level: | $264$ | $\SL_2$-level: | $4$ | ||||
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 | $2^{2}\cdot4^{2}$ | 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: | 4E0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}7&88\\26&37\end{bmatrix}$, $\begin{bmatrix}7&192\\199&191\end{bmatrix}$, $\begin{bmatrix}73&228\\44&199\end{bmatrix}$, $\begin{bmatrix}193&116\\231&31\end{bmatrix}$, $\begin{bmatrix}207&196\\107&101\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.12.0.s.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
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.1.3 | $8$ | $2$ | $2$ | $0$ | $0$ |
132.12.0-4.c.1.2 | $132$ | $2$ | $2$ | $0$ | $?$ |
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.cy.1.4 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.cy.1.13 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.cz.1.1 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.cz.1.16 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dk.1.6 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dk.1.11 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dl.1.4 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dl.1.13 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.do.1.8 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.do.1.9 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dp.1.2 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dp.1.15 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.ds.1.3 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.ds.1.14 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dt.1.2 | $264$ | $2$ | $2$ | $0$ |
264.48.0-264.dt.1.15 | $264$ | $2$ | $2$ | $0$ |
264.72.2-264.co.1.7 | $264$ | $3$ | $3$ | $2$ |
264.96.1-264.zm.1.9 | $264$ | $4$ | $4$ | $1$ |
264.288.9-264.ijq.1.6 | $264$ | $12$ | $12$ | $9$ |