Invariants
Level: | $260$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $5 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot10^{4}\cdot20^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
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: | 20I5 |
Level structure
$\GL_2(\Z/260\Z)$-generators: | $\begin{bmatrix}3&60\\96&101\end{bmatrix}$, $\begin{bmatrix}133&150\\157&69\end{bmatrix}$, $\begin{bmatrix}211&210\\157&119\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 260.144.5.hd.1 for the level structure with $-I$) |
Cyclic 260-isogeny field degree: | $28$ |
Cyclic 260-torsion field degree: | $672$ |
Full 260-torsion field degree: | $4193280$ |
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 |
---|---|---|---|---|---|
20.144.3-20.bk.2.7 | $20$ | $2$ | $2$ | $3$ | $0$ |
260.144.1-260.x.1.1 | $260$ | $2$ | $2$ | $1$ | $?$ |
260.144.1-260.x.1.7 | $260$ | $2$ | $2$ | $1$ | $?$ |
260.144.1-260.ba.2.11 | $260$ | $2$ | $2$ | $1$ | $?$ |
260.144.1-260.ba.2.14 | $260$ | $2$ | $2$ | $1$ | $?$ |
260.144.3-20.bk.2.5 | $260$ | $2$ | $2$ | $3$ | $?$ |