Invariants
| Level: | $190$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $1 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 2 }{2}$ | ||||||
| Cusps: | $2$ (all of which are rational) | Cusp widths | $2\cdot10$ | Cusp orbits | $1^{2}$ | ||
| 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: | 10A1 |
Level structure
| $\GL_2(\Z/190\Z)$-generators: | $\begin{bmatrix}49&102\\153&5\end{bmatrix}$, $\begin{bmatrix}68&135\\3&1\end{bmatrix}$, $\begin{bmatrix}171&148\\156&29\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 190-isogeny field degree: | $60$ |
| Cyclic 190-torsion field degree: | $4320$ |
| Full 190-torsion field degree: | $29548800$ |
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 |
|---|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 38.2.0.a.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 |
|---|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 38.2.0.a.1 | $38$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 190.24.1.c.1 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.24.1.c.2 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.24.1.e.1 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.24.1.e.2 | $190$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 190.36.1.b.1 | $190$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 190.60.3.f.1 | $190$ | $5$ | $5$ | $3$ | $?$ | not computed |
| 190.240.19.c.1 | $190$ | $20$ | $20$ | $19$ | $?$ | not computed |