Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | 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 | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
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: | 24V3 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}69&211\\88&63\end{bmatrix}$, $\begin{bmatrix}99&131\\26&213\end{bmatrix}$, $\begin{bmatrix}147&242\\16&263\end{bmatrix}$, $\begin{bmatrix}181&101\\180&239\end{bmatrix}$, $\begin{bmatrix}247&258\\0&223\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.3.rt.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 |
---|---|---|---|---|---|
12.96.1-12.o.1.3 | $12$ | $2$ | $2$ | $1$ | $0$ |
264.96.1-12.o.1.7 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.2-264.j.1.41 | $264$ | $2$ | $2$ | $2$ | $?$ |
264.96.2-264.j.1.54 | $264$ | $2$ | $2$ | $2$ | $?$ |
264.96.2-264.s.1.25 | $264$ | $2$ | $2$ | $2$ | $?$ |
264.96.2-264.s.1.54 | $264$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.384.9-264.bko.1.9 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.bkp.1.9 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.bkw.1.10 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.bkx.1.10 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.byv.1.1 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.byw.1.1 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.byz.1.14 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.bza.1.2 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.cir.1.2 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.cis.1.14 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.civ.1.13 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.ciw.1.13 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.crp.1.10 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.crq.1.10 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.crx.1.9 | $264$ | $2$ | $2$ | $9$ |
264.384.9-264.cry.1.9 | $264$ | $2$ | $2$ | $9$ |