Invariants
| Level: | $210$ | $\SL_2$-level: | $30$ | Newform level: | $1$ | ||
| Index: | $80$ | $\PSL_2$-index: | $40$ | ||||
| Genus: | $2 = 1 + \frac{ 40 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 2 }{2}$ | ||||||
| Cusps: | $2$ (all of which are rational) | Cusp widths | $10\cdot30$ | Cusp orbits | $1^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 30D2 |
Level structure
| $\GL_2(\Z/210\Z)$-generators: | $\begin{bmatrix}11&96\\17&103\end{bmatrix}$, $\begin{bmatrix}71&66\\56&139\end{bmatrix}$, $\begin{bmatrix}112&101\\19&3\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 210.40.2.c.1 for the level structure with $-I$) |
| Cyclic 210-isogeny field degree: | $144$ |
| Cyclic 210-torsion field degree: | $6912$ |
| Full 210-torsion field degree: | $3483648$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 30.40.1-15.a.1.4 | $30$ | $2$ | $2$ | $1$ | $0$ |
| 105.40.1-15.a.1.1 | $105$ | $2$ | $2$ | $1$ | $?$ |
| 210.16.0-210.a.1.7 | $210$ | $5$ | $5$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 210.240.8-210.d.1.7 | $210$ | $3$ | $3$ | $8$ |
| 210.240.8-210.h.1.13 | $210$ | $3$ | $3$ | $8$ |
| 210.240.9-210.p.1.2 | $210$ | $3$ | $3$ | $9$ |
| 210.320.9-210.bc.1.2 | $210$ | $4$ | $4$ | $9$ |