Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}39&40\\8&119\end{bmatrix}$, $\begin{bmatrix}71&213\\176&145\end{bmatrix}$, $\begin{bmatrix}147&248\\116&223\end{bmatrix}$, $\begin{bmatrix}151&199\\4&153\end{bmatrix}$, $\begin{bmatrix}171&155\\4&197\end{bmatrix}$, $\begin{bmatrix}235&159\\188&209\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 264.48.1-264.m.1.1, 264.48.1-264.m.1.2, 264.48.1-264.m.1.3, 264.48.1-264.m.1.4, 264.48.1-264.m.1.5, 264.48.1-264.m.1.6, 264.48.1-264.m.1.7, 264.48.1-264.m.1.8, 264.48.1-264.m.1.9, 264.48.1-264.m.1.10, 264.48.1-264.m.1.11, 264.48.1-264.m.1.12, 264.48.1-264.m.1.13, 264.48.1-264.m.1.14, 264.48.1-264.m.1.15, 264.48.1-264.m.1.16 |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
Full 264-torsion field degree: | $40550400$ |
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 |
---|---|---|---|---|---|---|
4.12.0.d.1 | $4$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.12.0.eu.1 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.12.1.dv.1 | $264$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.48.1.iw.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.ix.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.jj.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.jk.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.kl.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.km.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.lb.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.lg.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.me.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.mp.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.nk.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.nr.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.oa.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.oh.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.oq.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1.ot.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.72.5.by.1 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |
264.96.5.be.1 | $264$ | $4$ | $4$ | $5$ | $?$ | not computed |
264.288.21.be.1 | $264$ | $12$ | $12$ | $21$ | $?$ | not computed |