Invariants
Level: | $210$ | $\SL_2$-level: | $30$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $6^{4}\cdot30^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 30K9 |
Level structure
$\GL_2(\Z/210\Z)$-generators: | $\begin{bmatrix}29&119\\182&31\end{bmatrix}$, $\begin{bmatrix}32&47\\55&14\end{bmatrix}$, $\begin{bmatrix}163&59\\121&16\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 210-isogeny field degree: | $96$ |
Cyclic 210-torsion field degree: | $4608$ |
Full 210-torsion field degree: | $1935360$ |
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 |
---|---|---|---|---|---|
30.72.1.o.1 | $30$ | $2$ | $2$ | $1$ | $1$ |
105.72.3.t.2 | $105$ | $2$ | $2$ | $3$ | $?$ |
210.72.3.t.2 | $210$ | $2$ | $2$ | $3$ | $?$ |
210.72.5.dk.2 | $210$ | $2$ | $2$ | $5$ | $?$ |
210.72.5.dy.1 | $210$ | $2$ | $2$ | $5$ | $?$ |
210.72.5.ef.1 | $210$ | $2$ | $2$ | $5$ | $?$ |
210.72.5.eq.1 | $210$ | $2$ | $2$ | $5$ | $?$ |