Invariants
| Level: | $317$ | $\SL_2$-level: | $317$ | Newform level: | $1$ | ||
| Index: | $1327279$ | $\PSL_2$-index: | $1327279$ | ||||
| Genus: | $108459 = 1 + \frac{ 1327279 }{12} - \frac{ 79 }{4} - \frac{ 106 }{3} - \frac{ 4187 }{2}$ | ||||||
| Cusps: | $4187$ (none of which are rational) | Cusp widths | $317^{4187}$ | Cusp orbits | $79\cdot316^{13}$ | ||
| Elliptic points: | $79$ of order $2$ and $106$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $22140 \le \gamma \le 108459$ | ||||||
| $\overline{\Q}$-gonality: | $22140 \le \gamma \le 108459$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Sutherland (S) label: | 317S4 |
Level structure
| $\GL_2(\Z/317\Z)$-generators: | $\begin{bmatrix}65&133\\65&252\end{bmatrix}$, $\begin{bmatrix}248&258\\248&10\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 317-isogeny field degree: | $6$ |
| Cyclic 317-torsion field degree: | $1896$ |
| Full 317-torsion field degree: | $7584$ |
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 |
|---|---|---|---|---|---|
| $X(1)$ | $1$ | $1327279$ | $1327279$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 317.3981837.325481.a.1 | $317$ | $3$ | $3$ | $325481$ |
| 317.5309116.434018.b.1 | $317$ | $4$ | $4$ | $434018$ |