Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-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: | $\begin{bmatrix}27&140\\140&19\end{bmatrix}$, $\begin{bmatrix}87&55\\248&245\end{bmatrix}$, $\begin{bmatrix}115&222\\16&215\end{bmatrix}$, $\begin{bmatrix}137&237\\16&103\end{bmatrix}$, $\begin{bmatrix}229&137\\232&99\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.24.1.m.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
Full 264-torsion field degree: | $20275200$ |
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 |
---|---|---|---|---|---|---|
8.24.0-4.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.24.0-4.d.1.4 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
264.96.1-264.iw.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.ix.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.jj.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.jk.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.kl.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.km.1.7 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.lb.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.lg.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.me.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.mp.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.nk.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.nr.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.oa.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.oh.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.oq.1.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.96.1-264.ot.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.144.5-264.by.1.4 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |
264.192.5-264.be.1.20 | $264$ | $4$ | $4$ | $5$ | $?$ | not computed |