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 | $1^{2}\cdot2\cdot4\cdot8^{2}$ | 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: | 8I0 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}2&3\\123&74\end{bmatrix}$, $\begin{bmatrix}108&205\\235&134\end{bmatrix}$, $\begin{bmatrix}146&93\\189&74\end{bmatrix}$, $\begin{bmatrix}187&152\\166&85\end{bmatrix}$, $\begin{bmatrix}206&263\\57&44\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.24.0.bv.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
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 |
---|---|---|---|---|---|
24.24.0-8.n.1.7 | $24$ | $2$ | $2$ | $0$ | $0$ |
264.24.0-8.n.1.1 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
264.96.0-88.bb.1.1 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bc.2.4 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bd.2.1 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bf.1.8 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bh.2.1 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bi.2.8 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bk.1.1 | $264$ | $2$ | $2$ | $0$ |
264.96.0-88.bn.2.8 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.df.2.4 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dh.1.6 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dj.2.6 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.dl.1.8 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.eb.2.2 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.ee.1.6 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.ei.2.6 | $264$ | $2$ | $2$ | $0$ |
264.96.0-264.en.1.4 | $264$ | $2$ | $2$ | $0$ |
264.144.4-264.nv.1.22 | $264$ | $3$ | $3$ | $4$ |
264.192.3-264.pk.1.31 | $264$ | $4$ | $4$ | $3$ |