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: | $\begin{bmatrix}25&236\\108&233\end{bmatrix}$, $\begin{bmatrix}73&87\\24&187\end{bmatrix}$, $\begin{bmatrix}81&170\\136&125\end{bmatrix}$, $\begin{bmatrix}161&82\\72&19\end{bmatrix}$, $\begin{bmatrix}247&138\\196&257\end{bmatrix}$, $\begin{bmatrix}253&258\\204&205\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.48.1.za.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.1.11 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
264.48.0-12.g.1.12 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.0-264.fg.1.18 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.0-264.fg.1.29 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
264.48.1-264.hm.1.19 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.48.1-264.hm.1.26 | $264$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
264.192.1-264.rq.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rq.2.14 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rq.3.3 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rq.4.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rr.1.11 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rr.2.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rr.3.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.1-264.rr.4.10 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
264.192.3-264.kr.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.kr.2.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.kt.1.21 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.kt.2.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.lq.1.4 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.lr.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ly.1.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.lz.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mg.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mh.1.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.mk.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ml.1.4 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.oj.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.oj.2.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ol.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.192.3-264.ol.2.5 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
264.288.5-264.oa.1.21 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |