Invariants
| Level: | $269$ | $\SL_2$-level: | $269$ | Newform level: | $1$ | ||
| Index: | $811035$ | $\PSL_2$-index: | $811035$ | ||||
| Genus: | $66033 = 1 + \frac{ 811035 }{12} - \frac{ 67 }{4} - \frac{ 90 }{3} - \frac{ 3015 }{2}$ | ||||||
| Cusps: | $3015$ (none of which are rational) | Cusp widths | $269^{3015}$ | Cusp orbits | $67\cdot268^{11}$ | ||
| Elliptic points: | $67$ of order $2$ and $90$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $13533 \le \gamma \le 66033$ | ||||||
| $\overline{\Q}$-gonality: | $13533 \le \gamma \le 66033$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Sutherland (S) label: | 269S4 |
Level structure
| $\GL_2(\Z/269\Z)$-generators: | $\begin{bmatrix}0&155\\202&0\end{bmatrix}$, $\begin{bmatrix}87&129\\129&0\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 269-isogeny field degree: | $6$ |
| Cyclic 269-torsion field degree: | $1608$ |
| Full 269-torsion field degree: | $6432$ |
Rational points
This modular curve has real points and $\Q_p$ points for good $p < 8192$, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X(1)$ | $1$ | $811035$ | $811035$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 269.2433105.198187.a.1 | $269$ | $3$ | $3$ | $198187$ |
| 269.3244140.264286.b.1 | $269$ | $4$ | $4$ | $264286$ |