Invariants
| Level: | $28$ | $\SL_2$-level: | $4$ | ||||
| Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ 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: | 4E0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 28.12.0.14 |
Level structure
| $\GL_2(\Z/28\Z)$-generators: | $\begin{bmatrix}10&5\\27&12\end{bmatrix}$, $\begin{bmatrix}20&13\\21&26\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 56.24.0-28.f.1.1, 56.24.0-28.f.1.2, 56.24.0-28.f.1.3, 56.24.0-28.f.1.4, 168.24.0-28.f.1.1, 168.24.0-28.f.1.2, 168.24.0-28.f.1.3, 168.24.0-28.f.1.4, 280.24.0-28.f.1.1, 280.24.0-28.f.1.2, 280.24.0-28.f.1.3, 280.24.0-28.f.1.4 |
| Cyclic 28-isogeny field degree: | $16$ |
| Cyclic 28-torsion field degree: | $192$ |
| Full 28-torsion field degree: | $16128$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ 36 x^{2} - 448 y^{2} - 7 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 |
|---|---|---|---|---|---|
| 4.6.0.b.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
| 28.6.0.a.1 | $28$ | $2$ | $2$ | $0$ | $0$ |
| 28.6.0.d.1 | $28$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 28.96.5.j.1 | $28$ | $8$ | $8$ | $5$ |
| 28.252.16.r.1 | $28$ | $21$ | $21$ | $16$ |
| 28.336.21.r.1 | $28$ | $28$ | $28$ | $21$ |
| 84.36.2.r.1 | $84$ | $3$ | $3$ | $2$ |
| 84.48.1.j.1 | $84$ | $4$ | $4$ | $1$ |
| 140.60.4.j.1 | $140$ | $5$ | $5$ | $4$ |
| 140.72.3.n.1 | $140$ | $6$ | $6$ | $3$ |
| 140.120.7.r.1 | $140$ | $10$ | $10$ | $7$ |
| 252.324.22.z.1 | $252$ | $27$ | $27$ | $22$ |
| 308.144.9.j.1 | $308$ | $12$ | $12$ | $9$ |