Invariants
| Level: | $130$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $24$ | $\PSL_2$-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: | $\begin{bmatrix}30&53\\117&84\end{bmatrix}$, $\begin{bmatrix}57&115\\122&129\end{bmatrix}$, $\begin{bmatrix}75&1\\117&126\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 130.48.1-130.e.2.1, 130.48.1-130.e.2.2, 130.48.1-130.e.2.3, 130.48.1-130.e.2.4, 260.48.1-130.e.2.1, 260.48.1-130.e.2.2, 260.48.1-130.e.2.3, 260.48.1-130.e.2.4 |
| Cyclic 130-isogeny field degree: | $42$ |
| Cyclic 130-torsion field degree: | $2016$ |
| Full 130-torsion field degree: | $3144960$ |
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 |
|---|---|---|---|---|---|---|
| 10.12.0.a.1 | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 65.12.0.a.2 | $65$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 130.12.1.a.1 | $130$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 130.72.1.g.2 | $130$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 130.120.5.y.1 | $130$ | $5$ | $5$ | $5$ | $?$ | not computed |
| 260.96.5.s.1 | $260$ | $4$ | $4$ | $5$ | $?$ | not computed |