Invariants
Level: | $130$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
Index: | $120$ | $\PSL_2$-index: | $120$ | ||||
Genus: | $5 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{12}$ | Cusp orbits | $2^{2}\cdot8$ | ||
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: | 10A5 |
Level structure
$\GL_2(\Z/130\Z)$-generators: | $\begin{bmatrix}17&128\\82&117\end{bmatrix}$, $\begin{bmatrix}63&108\\77&113\end{bmatrix}$, $\begin{bmatrix}101&15\\65&16\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 130.240.5-130.z.1.1, 130.240.5-130.z.1.2, 130.240.5-130.z.1.3, 130.240.5-130.z.1.4, 260.240.5-130.z.1.1, 260.240.5-130.z.1.2, 260.240.5-130.z.1.3, 260.240.5-130.z.1.4 |
Cyclic 130-isogeny field degree: | $42$ |
Cyclic 130-torsion field degree: | $2016$ |
Full 130-torsion field degree: | $628992$ |
Rational points
This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
10.60.2.c.1 | $10$ | $2$ | $2$ | $2$ | $0$ |
65.60.0.b.1 | $65$ | $2$ | $2$ | $0$ | $0$ |
130.24.1.f.1 | $130$ | $5$ | $5$ | $1$ | $?$ |
130.24.1.f.2 | $130$ | $5$ | $5$ | $1$ | $?$ |
130.60.3.g.1 | $130$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
130.360.13.s.1 | $130$ | $3$ | $3$ | $13$ |