Invariants
Level: | $130$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $2^{2}\cdot10^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 24$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10D1 |
Level structure
$\GL_2(\Z/130\Z)$-generators: | $\begin{bmatrix}9&27\\28&25\end{bmatrix}$, $\begin{bmatrix}129&73\\79&110\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 130.24.1.e.2 for the level structure with $-I$) |
Cyclic 130-isogeny field degree: | $42$ |
Cyclic 130-torsion field degree: | $2016$ |
Full 130-torsion field degree: | $1572480$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
65.24.0-65.a.2.1 | $65$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
130.24.0-65.a.2.2 | $130$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
130.144.1-130.g.2.1 | $130$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
130.240.5-130.y.1.1 | $130$ | $5$ | $5$ | $5$ | $?$ | not computed |
260.192.5-260.s.1.5 | $260$ | $4$ | $4$ | $5$ | $?$ | not computed |