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: | $\begin{bmatrix}0&161\\193&188\end{bmatrix}$, $\begin{bmatrix}11&180\\126&29\end{bmatrix}$, $\begin{bmatrix}35&138\\128&121\end{bmatrix}$, $\begin{bmatrix}171&158\\236&213\end{bmatrix}$, $\begin{bmatrix}201&260\\92&201\end{bmatrix}$, $\begin{bmatrix}237&232\\178&3\end{bmatrix}$ |
| 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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $24$ | $12$ | $0$ | $0$ | full Jacobian |
| 88.24.0-88.z.1.12 | $88$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.48.0-12.g.1.12 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 88.24.0-88.z.1.12 | $88$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
| 264.48.0-12.g.1.5 | $264$ | $2$ | $2$ | $0$ | $?$ | 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.1.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.ra.2.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.ra.3.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.ra.4.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.rc.1.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.rc.2.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.rc.3.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.rc.4.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sk.1.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sk.2.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sk.3.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sk.4.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sm.1.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sm.2.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sm.3.28 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.sm.4.32 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.3-264.ff.1.18 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.fx.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.hh.1.33 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.hi.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.jl.1.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.jn.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.jx.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.jz.1.30 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.lt.1.47 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.lu.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.mi.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.ml.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.nd.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.ne.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.nk.1.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.nn.1.20 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.pv.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.pv.2.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.pv.3.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.pv.4.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.px.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.px.2.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.px.3.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.px.4.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qt.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qt.2.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qt.3.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qt.4.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qv.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qv.2.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qv.3.16 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.qv.4.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.288.5-264.pd.1.48 | $264$ | $3$ | $3$ | $5$ | $?$ | not computed |