Invariants
| Level: | $260$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot20^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20D5 |
Level structure
| $\GL_2(\Z/260\Z)$-generators: | $\begin{bmatrix}174&147\\185&141\end{bmatrix}$, $\begin{bmatrix}215&31\\194&117\end{bmatrix}$, $\begin{bmatrix}236&97\\27&121\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 260.96.5.m.2 for the level structure with $-I$) |
| Cyclic 260-isogeny field degree: | $84$ |
| Cyclic 260-torsion field degree: | $8064$ |
| Full 260-torsion field degree: | $6289920$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 20.96.3-20.i.2.6 | $20$ | $2$ | $2$ | $3$ | $0$ |
| 260.48.1-130.d.2.1 | $260$ | $4$ | $4$ | $1$ | $?$ |
| 260.96.3-20.i.2.2 | $260$ | $2$ | $2$ | $3$ | $?$ |