Invariants
| Level: | $266$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $4 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (none of which are rational) | Cusp widths | $2^{9}\cdot14^{9}$ | Cusp orbits | $3^{2}\cdot6^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 14B4 |
Level structure
| $\GL_2(\Z/266\Z)$-generators: | $\begin{bmatrix}152&167\\3&86\end{bmatrix}$, $\begin{bmatrix}160&183\\69&214\end{bmatrix}$, $\begin{bmatrix}198&183\\23&80\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 266.288.4-266.bg.1.1, 266.288.4-266.bg.1.2, 266.288.4-266.bg.1.3, 266.288.4-266.bg.1.4 |
| Cyclic 266-isogeny field degree: | $20$ |
| Cyclic 266-torsion field degree: | $2160$ |
| Full 266-torsion field degree: | $10342080$ |
Rational points
This modular curve has no $\Q_p$ points for $p=5$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 266.48.2.n.1 | $266$ | $3$ | $3$ | $2$ | $?$ |
| 266.48.2.t.1 | $266$ | $3$ | $3$ | $2$ | $?$ |
| 266.72.1.b.2 | $266$ | $2$ | $2$ | $1$ | $?$ |