Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | 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 | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | 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: | 12P1 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}21&260\\58&251\end{bmatrix}$, $\begin{bmatrix}49&42\\72&151\end{bmatrix}$, $\begin{bmatrix}93&98\\244&239\end{bmatrix}$, $\begin{bmatrix}151&174\\232&155\end{bmatrix}$, $\begin{bmatrix}209&168\\240&143\end{bmatrix}$, $\begin{bmatrix}241&192\\246&25\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.1.dh.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $3840$ |
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 |
---|---|---|---|---|---|---|
12.48.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.24.0-88.b.1.4 | $264$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
264.48.0-6.a.1.2 | $264$ | $2$ | $2$ | $0$ | $?$ | 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.lp.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lp.1.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lp.2.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lp.2.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lp.3.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lp.3.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lp.4.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lp.4.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.2.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.2.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.3.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.3.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.4.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.lr.4.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.3-264.cs.1.5 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cs.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ct.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ct.1.25 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cu.1.37 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cu.1.41 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cv.1.9 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.cv.1.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dh.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dh.1.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dj.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dj.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dn.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dn.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dp.1.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.dp.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ep.1.20 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ep.1.25 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ep.2.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ep.2.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.er.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.er.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.er.2.6 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.er.2.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fk.1.20 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fk.1.25 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fk.2.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fk.2.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fl.1.18 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fl.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fl.2.7 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.fl.2.22 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.288.5-264.d.1.16 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |