Invariants
| Level: | $258$ | $\SL_2$-level: | $6$ | Newform level: | $1$ | ||
| Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $6^{12}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| 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: | 6F1 |
Level structure
| $\GL_2(\Z/258\Z)$-generators: | $\begin{bmatrix}3&158\\26&21\end{bmatrix}$, $\begin{bmatrix}160&177\\117&232\end{bmatrix}$, $\begin{bmatrix}186&1\\217&42\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 258.144.1-258.d.1.1, 258.144.1-258.d.1.2 |
| Cyclic 258-isogeny field degree: | $44$ |
| Cyclic 258-torsion field degree: | $3696$ |
| Full 258-torsion field degree: | $13349952$ |
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 |
|---|---|---|---|---|---|---|
| $X_{\mathrm{sp}}(3)$ | $3$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
| 86.6.0.b.1 | $86$ | $12$ | $12$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 6.36.0.a.1 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 258.24.0.b.1 | $258$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 258.24.1.b.1 | $258$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 258.36.0.b.1 | $258$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 258.36.1.k.1 | $258$ | $2$ | $2$ | $1$ | $?$ | dimension zero |