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: | $\begin{bmatrix}15&230\\104&33\end{bmatrix}$, $\begin{bmatrix}106&113\\79&192\end{bmatrix}$, $\begin{bmatrix}193&180\\202&155\end{bmatrix}$, $\begin{bmatrix}222&247\\107&46\end{bmatrix}$, $\begin{bmatrix}225&98\\160&251\end{bmatrix}$, $\begin{bmatrix}231&214\\4&45\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.1.zx.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 |
264.24.0-264.bb.1.12 | $264$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
264.48.0-12.g.1.22 | $264$ | $2$ | $2$ | $0$ | $?$ | 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.ri.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ri.2.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ri.3.26 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ri.4.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rk.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rk.2.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rk.3.22 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rk.4.24 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ss.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ss.2.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ss.3.26 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.ss.4.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.su.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.su.2.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.su.3.22 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.su.4.24 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.3-264.fa.1.53 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fw.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ir.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.is.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.jk.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.jn.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.kf.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.kg.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.lw.1.22 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.lz.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mn.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mo.1.10 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mu.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mx.1.20 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.nx.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ny.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qd.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qd.2.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qd.3.12 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qd.4.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qf.1.12 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qf.2.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qf.3.22 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.qf.4.28 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rb.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rb.2.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rb.3.12 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rb.4.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rd.1.12 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rd.2.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rd.3.22 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.rd.4.28 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.288.5-264.pg.1.47 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |