Invariants
| Level: | $260$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20G3 |
Level structure
| $\GL_2(\Z/260\Z)$-generators: | $\begin{bmatrix}12&217\\143&106\end{bmatrix}$, $\begin{bmatrix}50&9\\131&218\end{bmatrix}$, $\begin{bmatrix}77&14\\66&195\end{bmatrix}$, $\begin{bmatrix}190&219\\253&126\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 260.72.3.cn.2 for the level structure with $-I$) |
| Cyclic 260-isogeny field degree: | $28$ |
| Cyclic 260-torsion field degree: | $1344$ |
| Full 260-torsion field degree: | $8386560$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.72.0-10.a.2.4 | $10$ | $2$ | $2$ | $0$ | $0$ |
| 260.72.0-10.a.2.6 | $260$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 260.288.5-260.e.1.4 | $260$ | $2$ | $2$ | $5$ |
| 260.288.5-260.bg.1.5 | $260$ | $2$ | $2$ | $5$ |
| 260.288.5-260.cm.1.6 | $260$ | $2$ | $2$ | $5$ |
| 260.288.5-260.cr.1.5 | $260$ | $2$ | $2$ | $5$ |
| 260.288.5-260.dk.1.1 | $260$ | $2$ | $2$ | $5$ |
| 260.288.5-260.du.1.5 | $260$ | $2$ | $2$ | $5$ |
| 260.288.5-260.ea.1.7 | $260$ | $2$ | $2$ | $5$ |
| 260.288.5-260.ef.1.5 | $260$ | $2$ | $2$ | $5$ |