Invariants
| Level: | $264$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot4^{3}\cdot8$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| 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: | 8J0 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}25&64\\226&245\end{bmatrix}$, $\begin{bmatrix}33&136\\214&19\end{bmatrix}$, $\begin{bmatrix}71&228\\156&167\end{bmatrix}$, $\begin{bmatrix}155&220\\184&199\end{bmatrix}$, $\begin{bmatrix}231&92\\20&143\end{bmatrix}$, $\begin{bmatrix}251&156\\16&125\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.24.0.t.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $96$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $20275200$ |
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 |
|---|---|---|---|---|---|
| 8.24.0-4.b.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 264.24.0-4.b.1.3 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.