Invariants
| Level: | $139$ | $\SL_2$-level: | $139$ | Newform level: | $1$ | ||
| Index: | $111895$ | $\PSL_2$-index: | $111895$ | ||||
| Genus: | $8899 = 1 + \frac{ 111895 }{12} - \frac{ 35 }{4} - \frac{ 46 }{3} - \frac{ 805 }{2}$ | ||||||
| Cusps: | $805$ (none of which are rational) | Cusp widths | $139^{805}$ | Cusp orbits | $46\cdot69\cdot138^{5}$ | ||
| Elliptic points: | $35$ of order $2$ and $46$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $1873 \le \gamma \le 8899$ | ||||||
| $\overline{\Q}$-gonality: | $1873 \le \gamma \le 8899$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Sutherland (S) label: | 139S4 |
Level structure
| $\GL_2(\Z/139\Z)$-generators: | $\begin{bmatrix}125&107\\18&14\end{bmatrix}$, $\begin{bmatrix}135&0\\135&33\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 139-isogeny field degree: | $8$ |
| Cyclic 139-torsion field degree: | $1104$ |
| Full 139-torsion field degree: | $3312$ |
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 |
|---|---|---|---|---|---|
| $X(1)$ | $1$ | $111895$ | $111895$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 139.335685.26741.a.1 | $139$ | $3$ | $3$ | $26741$ |
| 139.447580.35674.m.1 | $139$ | $4$ | $4$ | $35674$ |