Invariants
| Level: | $190$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $180$ | $\PSL_2$-index: | $180$ | ||||
| Genus: | $7 = 1 + \frac{ 180 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (of which $2$ are rational) | Cusp widths | $10^{18}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10A7 |
Level structure
| $\GL_2(\Z/190\Z)$-generators: | $\begin{bmatrix}9&188\\11&151\end{bmatrix}$, $\begin{bmatrix}49&34\\143&165\end{bmatrix}$, $\begin{bmatrix}185&158\\6&97\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 190-isogeny field degree: | $20$ |
| Cyclic 190-torsion field degree: | $1440$ |
| Full 190-torsion field degree: | $1969920$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{sp}}(5)$ | $5$ | $6$ | $6$ | $0$ | $0$ |
| 38.6.0.b.1 | $38$ | $30$ | $30$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.90.2.a.1 | $10$ | $2$ | $2$ | $2$ | $0$ |
| 190.36.1.b.1 | $190$ | $5$ | $5$ | $1$ | $?$ |
| 190.60.3.f.1 | $190$ | $3$ | $3$ | $3$ | $?$ |
| 190.90.3.b.1 | $190$ | $2$ | $2$ | $3$ | $?$ |
| 190.90.4.b.1 | $190$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 190.360.13.i.1 | $190$ | $2$ | $2$ | $13$ |
| 190.360.13.r.1 | $190$ | $2$ | $2$ | $13$ |