Invariants
Level: | $28$ | $\SL_2$-level: | $4$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 4G0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 28.48.0.12 |
Level structure
$\GL_2(\Z/28\Z)$-generators: | $\begin{bmatrix}17&6\\14&15\end{bmatrix}$, $\begin{bmatrix}23&24\\20&25\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 28.24.0.b.1 for the level structure with $-I$) |
Cyclic 28-isogeny field degree: | $16$ |
Cyclic 28-torsion field degree: | $96$ |
Full 28-torsion field degree: | $4032$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 2 x^{2} + 3 x y + 9 y^{2} + 28 z^{2} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
4.24.0-4.a.1.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
28.24.0-4.a.1.2 | $28$ | $2$ | $2$ | $0$ | $0$ |
28.24.0-28.b.1.1 | $28$ | $2$ | $2$ | $0$ | $0$ |
28.24.0-28.b.1.2 | $28$ | $2$ | $2$ | $0$ | $0$ |
28.24.0-28.b.1.3 | $28$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
28.384.11-28.d.1.1 | $28$ | $8$ | $8$ | $11$ |
28.1008.34-28.d.1.1 | $28$ | $21$ | $21$ | $34$ |
28.1344.45-28.d.1.1 | $28$ | $28$ | $28$ | $45$ |
56.96.1-56.j.1.1 | $56$ | $2$ | $2$ | $1$ |
56.96.1-56.k.1.1 | $56$ | $2$ | $2$ | $1$ |
56.96.1-56.bp.1.2 | $56$ | $2$ | $2$ | $1$ |
56.96.1-56.bq.1.1 | $56$ | $2$ | $2$ | $1$ |
84.144.4-84.b.1.1 | $84$ | $3$ | $3$ | $4$ |
84.192.3-84.b.1.1 | $84$ | $4$ | $4$ | $3$ |
140.240.8-140.b.1.1 | $140$ | $5$ | $5$ | $8$ |
140.288.7-140.d.1.1 | $140$ | $6$ | $6$ | $7$ |
140.480.15-140.b.1.2 | $140$ | $10$ | $10$ | $15$ |
168.96.1-168.bk.1.1 | $168$ | $2$ | $2$ | $1$ |
168.96.1-168.bm.1.1 | $168$ | $2$ | $2$ | $1$ |
168.96.1-168.eu.1.1 | $168$ | $2$ | $2$ | $1$ |
168.96.1-168.ew.1.2 | $168$ | $2$ | $2$ | $1$ |
280.96.1-280.bk.1.2 | $280$ | $2$ | $2$ | $1$ |
280.96.1-280.bm.1.1 | $280$ | $2$ | $2$ | $1$ |
280.96.1-280.eq.1.1 | $280$ | $2$ | $2$ | $1$ |
280.96.1-280.es.1.1 | $280$ | $2$ | $2$ | $1$ |