Invariants
| Level: | $190$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $36$ | $\PSL_2$-index: | $36$ | ||||
| Genus: | $1 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{3}\cdot10^{3}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ 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: | 10G1 |
Level structure
| $\GL_2(\Z/190\Z)$-generators: | $\begin{bmatrix}2&31\\47&188\end{bmatrix}$, $\begin{bmatrix}148&79\\35&184\end{bmatrix}$, $\begin{bmatrix}165&82\\168&11\end{bmatrix}$ |
| 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: | $9849600$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
| 38.6.0.b.1 | $38$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_0(10)$ | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 38.6.0.b.1 | $38$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
| 190.12.1.a.1 | $190$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 190.72.1.e.1 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.72.1.e.2 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.72.1.g.1 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.72.1.g.2 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.180.7.i.1 | $190$ | $5$ | $5$ | $7$ | $?$ | not computed |