Invariants
| Level: | $260$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $72$ | $\PSL_2$-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: | $\begin{bmatrix}73&176\\240&79\end{bmatrix}$, $\begin{bmatrix}77&24\\188&203\end{bmatrix}$, $\begin{bmatrix}117&112\\218&201\end{bmatrix}$, $\begin{bmatrix}125&64\\204&35\end{bmatrix}$, $\begin{bmatrix}170&61\\47&54\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 260.144.3-260.cn.2.1, 260.144.3-260.cn.2.2, 260.144.3-260.cn.2.3, 260.144.3-260.cn.2.4, 260.144.3-260.cn.2.5, 260.144.3-260.cn.2.6, 260.144.3-260.cn.2.7, 260.144.3-260.cn.2.8, 260.144.3-260.cn.2.9, 260.144.3-260.cn.2.10, 260.144.3-260.cn.2.11, 260.144.3-260.cn.2.12, 260.144.3-260.cn.2.13, 260.144.3-260.cn.2.14, 260.144.3-260.cn.2.15, 260.144.3-260.cn.2.16 |
| Cyclic 260-isogeny field degree: | $28$ |
| Cyclic 260-torsion field degree: | $1344$ |
| Full 260-torsion field degree: | $16773120$ |
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 |
|---|---|---|---|---|---|
| $X_{\pm1}(10)$ | $10$ | $2$ | $2$ | $0$ | $0$ |
| 260.36.1.h.1 | $260$ | $2$ | $2$ | $1$ | $?$ |
| 260.36.2.a.2 | $260$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 260.144.5.e.1 | $260$ | $2$ | $2$ | $5$ |
| 260.144.5.bg.1 | $260$ | $2$ | $2$ | $5$ |
| 260.144.5.cm.1 | $260$ | $2$ | $2$ | $5$ |
| 260.144.5.cr.1 | $260$ | $2$ | $2$ | $5$ |
| 260.144.5.dk.1 | $260$ | $2$ | $2$ | $5$ |
| 260.144.5.du.1 | $260$ | $2$ | $2$ | $5$ |
| 260.144.5.ea.1 | $260$ | $2$ | $2$ | $5$ |
| 260.144.5.ef.1 | $260$ | $2$ | $2$ | $5$ |
| 260.360.19.hs.1 | $260$ | $5$ | $5$ | $19$ |