Invariants
| Level: | $266$ | $\SL_2$-level: | $38$ | Newform level: | $1$ | ||
| Index: | $360$ | $\PSL_2$-index: | $360$ | ||||
| Genus: | $22 = 1 + \frac{ 360 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (none of which are rational) | Cusp widths | $2^{9}\cdot38^{9}$ | Cusp orbits | $3^{2}\cdot6^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 42$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 22$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 38C22 |
Level structure
| $\GL_2(\Z/266\Z)$-generators: | $\begin{bmatrix}144&97\\149&44\end{bmatrix}$, $\begin{bmatrix}199&82\\120&47\end{bmatrix}$, $\begin{bmatrix}204&239\\107&224\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 266-isogeny field degree: | $8$ |
| Cyclic 266-torsion field degree: | $864$ |
| Full 266-torsion field degree: | $4136832$ |
Rational points
This modular curve has no $\Q_p$ points for $p=11,43,139$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 38.120.8.e.1 | $38$ | $3$ | $3$ | $8$ | $2$ |
| 266.120.4.n.2 | $266$ | $3$ | $3$ | $4$ | $?$ |
| 266.180.10.c.1 | $266$ | $2$ | $2$ | $10$ | $?$ |