Invariants
| Level: | $266$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $42$ | $\PSL_2$-index: | $42$ | ||||
| Genus: | $3 = 1 + \frac{ 42 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 3 }{2}$ | ||||||
| Cusps: | $3$ (none of which are rational) | Cusp widths | $14^{3}$ | Cusp orbits | $3$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 14A3 |
Level structure
| $\GL_2(\Z/266\Z)$-generators: | $\begin{bmatrix}9&58\\127&215\end{bmatrix}$, $\begin{bmatrix}109&195\\155&218\end{bmatrix}$, $\begin{bmatrix}226&223\\75&5\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 266-isogeny field degree: | $480$ |
| Cyclic 266-torsion field degree: | $51840$ |
| Full 266-torsion field degree: | $35458560$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(7)$ | $7$ | $2$ | $2$ | $0$ | $0$ |
| 38.2.0.a.1 | $38$ | $21$ | $21$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(7)$ | $7$ | $2$ | $2$ | $0$ | $0$ |
| 38.2.0.a.1 | $38$ | $21$ | $21$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 266.84.5.e.1 | $266$ | $2$ | $2$ | $5$ |
| 266.84.5.g.1 | $266$ | $2$ | $2$ | $5$ |
| 266.84.5.j.1 | $266$ | $2$ | $2$ | $5$ |
| 266.84.5.l.1 | $266$ | $2$ | $2$ | $5$ |
| 266.126.7.d.1 | $266$ | $3$ | $3$ | $7$ |