Invariants
| Level: | $266$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $252$ | $\PSL_2$-index: | $252$ | ||||
| Genus: | $13 = 1 + \frac{ 252 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (none of which are rational) | Cusp widths | $14^{18}$ | Cusp orbits | $3^{2}\cdot6^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 13$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 14A13 |
Level structure
| $\GL_2(\Z/266\Z)$-generators: | $\begin{bmatrix}23&200\\210&61\end{bmatrix}$, $\begin{bmatrix}178&251\\5&62\end{bmatrix}$, $\begin{bmatrix}248&97\\259&228\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 266-isogeny field degree: | $80$ |
| Cyclic 266-torsion field degree: | $8640$ |
| Full 266-torsion field degree: | $5909760$ |
Rational points
This modular curve has no $\Q_p$ points for $p=5,17$, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 7.42.1.b.1 | $7$ | $6$ | $6$ | $1$ | $0$ |
| 38.6.0.b.1 | $38$ | $42$ | $42$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 14.126.5.b.1 | $14$ | $2$ | $2$ | $5$ | $0$ |
| 266.84.5.g.1 | $266$ | $3$ | $3$ | $5$ | $?$ |
| 266.126.5.c.1 | $266$ | $2$ | $2$ | $5$ | $?$ |
| 266.126.7.d.1 | $266$ | $2$ | $2$ | $7$ | $?$ |