Invariants
Level: | $210$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
Index: | $60$ | $\PSL_2$-index: | $60$ | ||||
Genus: | $3 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $10^{6}$ | Cusp orbits | $2\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10B3 |
Level structure
$\GL_2(\Z/210\Z)$-generators: | $\begin{bmatrix}61&84\\156&1\end{bmatrix}$, $\begin{bmatrix}67&85\\185&148\end{bmatrix}$, $\begin{bmatrix}197&192\\133&127\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 210-isogeny field degree: | $192$ |
Cyclic 210-torsion field degree: | $9216$ |
Full 210-torsion field degree: | $4644864$ |
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 |
---|---|---|---|---|---|
30.30.1.c.1 | $30$ | $2$ | $2$ | $1$ | $0$ |
70.30.2.e.1 | $70$ | $2$ | $2$ | $2$ | $1$ |
105.30.0.b.1 | $105$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
210.180.7.bl.1 | $210$ | $3$ | $3$ | $7$ |
210.180.13.ib.1 | $210$ | $3$ | $3$ | $13$ |
210.240.15.bx.1 | $210$ | $4$ | $4$ | $15$ |