Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot3^{4}\cdot8\cdot24$ | Cusp orbits | $1^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24B0 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}157&84\\228&247\end{bmatrix}$, $\begin{bmatrix}174&223\\199&144\end{bmatrix}$, $\begin{bmatrix}196&189\\209&74\end{bmatrix}$, $\begin{bmatrix}203&38\\70&153\end{bmatrix}$, $\begin{bmatrix}237&98\\158&189\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.0.dn.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $48$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $10137600$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.48.0-12.f.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 264.48.0-12.f.1.15 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.192.3-264.dq.1.3 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.fy.1.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.gk.2.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.gq.2.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.jc.1.11 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.jf.1.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.jg.1.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.jj.1.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.oa.2.3 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.od.2.1 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.oe.2.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.oh.2.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.oq.1.11 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.ot.1.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.ou.1.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.ox.1.13 | $264$ | $2$ | $2$ | $3$ |
| 264.288.3-264.d.1.29 | $264$ | $3$ | $3$ | $3$ |