Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}55&60\\224&65\end{bmatrix}$, $\begin{bmatrix}125&232\\188&17\end{bmatrix}$, $\begin{bmatrix}213&100\\16&263\end{bmatrix}$, $\begin{bmatrix}225&208\\176&159\end{bmatrix}$, $\begin{bmatrix}261&112\\136&143\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.96.1.x.2 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $3840$ |
Full 264-torsion field degree: | $5068800$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.96.0-8.c.1.9 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.96.0-88.b.1.5 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.b.1.18 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-8.c.1.7 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.u.2.1 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.u.2.16 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.v.2.5 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.v.2.12 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.1-88.o.2.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.o.2.12 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.be.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.be.1.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.bf.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.bf.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
264.384.5-88.x.1.6 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-88.y.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-88.ba.1.4 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-88.bb.4.5 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hi.1.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hk.1.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hs.1.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hu.2.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |