Invariants
| Level: | $28$ | $\SL_2$-level: | $4$ | ||||
| Index: | $8$ | $\PSL_2$-index: | $8$ | ||||
| Genus: | $0 = 1 + \frac{ 8 }{12} - \frac{ 0 }{4} - \frac{ 2 }{3} - \frac{ 2 }{2}$ | ||||||
| Cusps: | $2$ (none of which are rational) | Cusp widths | $4^{2}$ | Cusp orbits | $2$ | ||
| Elliptic points: | $0$ of order $2$ and $2$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4D0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 28.8.0.1 |
Level structure
| $\GL_2(\Z/28\Z)$-generators: | $\begin{bmatrix}5&22\\3&3\end{bmatrix}$, $\begin{bmatrix}20&17\\13&9\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 28-isogeny field degree: | $48$ |
| Cyclic 28-torsion field degree: | $576$ |
| Full 28-torsion field degree: | $24192$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ 18 x^{2} + 6 x z - 1008 y^{2} + 112 y z - 3 z^{2} $ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(4)$ | $4$ | $2$ | $2$ | $0$ | $0$ |
| 14.2.0.a.1 | $14$ | $4$ | $4$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 28.24.0.f.1 | $28$ | $3$ | $3$ | $0$ |
| 28.64.3.c.1 | $28$ | $8$ | $8$ | $3$ |
| 28.168.12.c.1 | $28$ | $21$ | $21$ | $12$ |
| 28.224.15.c.1 | $28$ | $28$ | $28$ | $15$ |
| 56.32.1.a.1 | $56$ | $4$ | $4$ | $1$ |
| 84.24.2.a.1 | $84$ | $3$ | $3$ | $2$ |
| 84.32.1.a.1 | $84$ | $4$ | $4$ | $1$ |
| 140.40.2.a.1 | $140$ | $5$ | $5$ | $2$ |
| 140.48.3.e.1 | $140$ | $6$ | $6$ | $3$ |
| 140.80.5.a.1 | $140$ | $10$ | $10$ | $5$ |
| 252.216.14.a.1 | $252$ | $27$ | $27$ | $14$ |
| 308.96.7.a.1 | $308$ | $12$ | $12$ | $7$ |