Invariants
| Level: | $101$ | $\SL_2$-level: | $101$ | Newform level: | $1$ | ||
| Index: | $42925$ | $\PSL_2$-index: | $42925$ | ||||
| Genus: | $3348 = 1 + \frac{ 42925 }{12} - \frac{ 25 }{4} - \frac{ 34 }{3} - \frac{ 425 }{2}$ | ||||||
| Cusps: | $425$ (none of which are rational) | Cusp widths | $101^{425}$ | Cusp orbits | $25\cdot100^{4}$ | ||
| Elliptic points: | $25$ of order $2$ and $34$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $722 \le \gamma \le 3348$ | ||||||
| $\overline{\Q}$-gonality: | $722 \le \gamma \le 3348$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Sutherland (S) label: | 101S4 |
Level structure
| $\GL_2(\Z/101\Z)$-generators: | $\begin{bmatrix}0&23\\28&96\end{bmatrix}$, $\begin{bmatrix}9&2\\11&92\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 101-isogeny field degree: | $6$ |
| Cyclic 101-torsion field degree: | $600$ |
| Full 101-torsion field degree: | $2400$ |
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 |
|---|---|---|---|---|---|
| $X(1)$ | $1$ | $42925$ | $42925$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 101.128775.10076.a.1 | $101$ | $3$ | $3$ | $10076$ |
| 101.171700.13448.b.1 | $101$ | $4$ | $4$ | $13448$ |