Invariants
| Level: | $157$ | $\SL_2$-level: | $157$ | Newform level: | $1$ | ||
| Index: | $161239$ | $\PSL_2$-index: | $161239$ | ||||
| Genus: | $12897 = 1 + \frac{ 161239 }{12} - \frac{ 39 }{4} - \frac{ 52 }{3} - \frac{ 1027 }{2}$ | ||||||
| Cusps: | $1027$ (none of which are rational) | Cusp widths | $157^{1027}$ | Cusp orbits | $39\cdot52\cdot156^{6}$ | ||
| Elliptic points: | $39$ of order $2$ and $52$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2697 \le \gamma \le 12897$ | ||||||
| $\overline{\Q}$-gonality: | $2697 \le \gamma \le 12897$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Sutherland (S) label: | 157S4 |
Level structure
| $\GL_2(\Z/157\Z)$-generators: | $\begin{bmatrix}3&154\\3&0\end{bmatrix}$, $\begin{bmatrix}17&130\\147&37\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 157-isogeny field degree: | $6$ |
| Cyclic 157-torsion field degree: | $936$ |
| Full 157-torsion field degree: | $3744$ |
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 |
|---|---|---|---|---|---|
| $X(1)$ | $1$ | $161239$ | $161239$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 157.483717.38741.a.1 | $157$ | $3$ | $3$ | $38741$ |
| 157.644956.51676.n.1 | $157$ | $4$ | $4$ | $51676$ |