Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12K3 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}49&4\\66&107\end{bmatrix}$, $\begin{bmatrix}81&244\\164&35\end{bmatrix}$, $\begin{bmatrix}123&250\\74&53\end{bmatrix}$, $\begin{bmatrix}171&10\\140&125\end{bmatrix}$, $\begin{bmatrix}261&146\\224&261\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.3.dg.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $5068800$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.96.1-24.by.1.20 | $24$ | $2$ | $2$ | $1$ | $0$ |
132.96.1-132.c.1.18 | $132$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-132.c.1.11 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-24.by.1.12 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.dg.1.16 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.dg.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.384.5-264.jy.1.7 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.jy.2.13 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.jy.3.11 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.jy.4.11 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kb.1.13 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kb.2.13 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kb.3.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.kb.4.16 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pk.1.5 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pk.2.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pk.3.9 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pk.4.15 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.1.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.2.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.3.14 | $264$ | $2$ | $2$ | $5$ |
264.384.5-264.pn.4.15 | $264$ | $2$ | $2$ | $5$ |