Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
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: | 24G1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}41&18\\168&239\end{bmatrix}$, $\begin{bmatrix}80&99\\255&32\end{bmatrix}$, $\begin{bmatrix}114&241\\77&214\end{bmatrix}$, $\begin{bmatrix}172&15\\39&4\end{bmatrix}$, $\begin{bmatrix}192&197\\65&36\end{bmatrix}$, $\begin{bmatrix}260&7\\213&190\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.1.zt.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $24$ |
Cyclic 264-torsion field degree: | $1920$ |
Full 264-torsion field degree: | $10137600$ |
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 |
---|---|---|---|---|---|---|
12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.24.0-88.z.1.16 | $264$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
264.48.0-12.g.1.21 | $264$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.192.1-264.ra.1.23 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ra.2.21 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ra.3.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ra.4.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rc.1.22 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rc.2.18 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rc.3.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rc.4.11 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sk.1.23 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sk.2.21 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sk.3.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sk.4.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sm.1.23 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sm.2.19 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sm.3.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.sm.4.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.3-264.ff.1.55 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fx.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.hh.1.5 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.hi.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.jl.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.jn.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.jx.1.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.jz.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.lt.1.9 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.lu.1.5 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mi.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ml.1.5 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.nd.1.7 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ne.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.nk.1.12 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.nn.1.20 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.pv.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.pv.2.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.pv.3.22 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.pv.4.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.px.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.px.2.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.px.3.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.px.4.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qt.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qt.2.18 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qt.3.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qt.4.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qv.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qv.2.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qv.3.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qv.4.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.288.5-264.pd.1.21 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |