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: | $\begin{bmatrix}71&84\\84&65\end{bmatrix}$, $\begin{bmatrix}73&120\\236&151\end{bmatrix}$, $\begin{bmatrix}155&160\\76&103\end{bmatrix}$, $\begin{bmatrix}189&80\\236&31\end{bmatrix}$, $\begin{bmatrix}211&144\\252&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.96.1.w.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.1.7 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.96.0-88.b.2.11 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.b.2.23 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-8.c.1.1 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.q.2.4 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.q.2.14 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.r.2.4 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.0-88.r.2.13 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.96.1-88.n.2.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.n.2.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.bi.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.bi.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.bj.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-88.bj.1.13 | $264$ | $2$ | $2$ | $1$ | $?$ | 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.w.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-88.y.2.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-88.z.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-88.bb.2.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hh.2.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hj.2.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.hq.2.10 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
264.384.5-264.ht.2.13 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |