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: | $6$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
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: | 8G0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}91&168\\111&5\end{bmatrix}$, $\begin{bmatrix}125&232\\38&225\end{bmatrix}$, $\begin{bmatrix}129&208\\146&247\end{bmatrix}$, $\begin{bmatrix}165&208\\193&105\end{bmatrix}$, $\begin{bmatrix}191&248\\193&231\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.24.0.bj.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $20275200$ |
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 |
---|---|---|---|---|---|
24.24.0-8.n.1.4 | $24$ | $2$ | $2$ | $0$ | $0$ |
264.24.0-8.n.1.8 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.96.0-88.bk.1.4 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bk.1.6 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bk.2.4 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bk.2.7 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bl.1.4 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bl.1.6 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bl.2.4 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bl.2.7 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dv.1.6 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dv.1.15 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dv.2.7 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dv.2.9 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dw.1.8 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dw.1.13 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dw.2.3 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dw.2.13 | $264$ | $2$ | $2$ | $0$ |
264.144.4-264.iv.1.14 | $264$ | $3$ | $3$ | $4$ |
264.192.3-264.lt.1.10 | $264$ | $4$ | $4$ | $3$ |