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: | $\begin{bmatrix}11&256\\74&105\end{bmatrix}$, $\begin{bmatrix}21&8\\88&71\end{bmatrix}$, $\begin{bmatrix}79&206\\96&173\end{bmatrix}$, $\begin{bmatrix}95&154\\92&69\end{bmatrix}$, $\begin{bmatrix}103&74\\210&155\end{bmatrix}$, $\begin{bmatrix}263&106\\146&207\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.1.dg.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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 3.8.0-3.a.1.1 | $3$ | $12$ | $12$ | $0$ | $0$ | full Jacobian |
| 88.12.0.a.1 | $88$ | $8$ | $4$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 6.48.0-6.a.1.2 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 264.48.0-6.a.1.5 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 264.48.0-264.fi.1.12 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 264.48.0-264.fi.1.21 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 264.48.1-264.hn.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.48.1-264.hn.1.25 | $264$ | $2$ | $2$ | $1$ | $?$ | 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.lm.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.lm.2.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.lm.3.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.lm.4.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.lo.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.lo.2.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.lo.3.8 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.lo.4.16 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.3-264.cq.1.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.cr.1.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.cu.1.48 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.cw.1.30 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.de.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dg.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dk.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dm.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.em.1.11 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.em.2.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.eo.1.12 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.eo.2.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.fh.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.fh.2.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.fi.1.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.fi.2.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.288.5-264.a.1.1 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |