Invariants
Level: | $20$ | $\SL_2$-level: | $5$ | ||||
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 | $1^{2}\cdot5^{2}$ | Cusp orbits | $2^{2}$ | ||
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: | 5D0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 20.12.0.23 |
Level structure
$\GL_2(\Z/20\Z)$-generators: | $\begin{bmatrix}1&3\\19&10\end{bmatrix}$, $\begin{bmatrix}1&8\\1&19\end{bmatrix}$, $\begin{bmatrix}11&4\\19&7\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 20-isogeny field degree: | $6$ |
Cyclic 20-torsion field degree: | $48$ |
Full 20-torsion field degree: | $3840$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 5 x^{2} + 100 x y + 520 y^{2} + z^{2} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
|
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_0(5)$ | $5$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
20.24.1.a.2 | $20$ | $2$ | $2$ | $1$ |
20.24.1.c.2 | $20$ | $2$ | $2$ | $1$ |
20.24.1.d.2 | $20$ | $2$ | $2$ | $1$ |
20.24.1.f.1 | $20$ | $2$ | $2$ | $1$ |
20.36.0.a.1 | $20$ | $3$ | $3$ | $0$ |
20.48.3.j.2 | $20$ | $4$ | $4$ | $3$ |
20.60.0.a.1 | $20$ | $5$ | $5$ | $0$ |
40.24.1.ca.2 | $40$ | $2$ | $2$ | $1$ |
40.24.1.cg.2 | $40$ | $2$ | $2$ | $1$ |
40.24.1.cm.2 | $40$ | $2$ | $2$ | $1$ |
40.24.1.cs.1 | $40$ | $2$ | $2$ | $1$ |
60.24.1.j.2 | $60$ | $2$ | $2$ | $1$ |
60.24.1.l.1 | $60$ | $2$ | $2$ | $1$ |
60.24.1.bc.2 | $60$ | $2$ | $2$ | $1$ |
60.24.1.be.2 | $60$ | $2$ | $2$ | $1$ |
60.36.2.fs.1 | $60$ | $3$ | $3$ | $2$ |
60.48.1.bw.1 | $60$ | $4$ | $4$ | $1$ |
100.60.0.a.2 | $100$ | $5$ | $5$ | $0$ |
120.24.1.eq.2 | $120$ | $2$ | $2$ | $1$ |
120.24.1.ew.1 | $120$ | $2$ | $2$ | $1$ |
120.24.1.jo.2 | $120$ | $2$ | $2$ | $1$ |
120.24.1.ju.2 | $120$ | $2$ | $2$ | $1$ |
140.24.1.h.2 | $140$ | $2$ | $2$ | $1$ |
140.24.1.i.1 | $140$ | $2$ | $2$ | $1$ |
140.24.1.k.2 | $140$ | $2$ | $2$ | $1$ |
140.24.1.l.2 | $140$ | $2$ | $2$ | $1$ |
140.96.5.ca.1 | $140$ | $8$ | $8$ | $5$ |
140.252.16.dg.1 | $140$ | $21$ | $21$ | $16$ |
140.336.21.dg.2 | $140$ | $28$ | $28$ | $21$ |
180.324.22.hq.1 | $180$ | $27$ | $27$ | $22$ |
220.24.1.h.2 | $220$ | $2$ | $2$ | $1$ |
220.24.1.i.2 | $220$ | $2$ | $2$ | $1$ |
220.24.1.k.2 | $220$ | $2$ | $2$ | $1$ |
220.24.1.l.2 | $220$ | $2$ | $2$ | $1$ |
220.144.9.bk.1 | $220$ | $12$ | $12$ | $9$ |
260.24.1.h.2 | $260$ | $2$ | $2$ | $1$ |
260.24.1.i.2 | $260$ | $2$ | $2$ | $1$ |
260.24.1.k.2 | $260$ | $2$ | $2$ | $1$ |
260.24.1.l.1 | $260$ | $2$ | $2$ | $1$ |
260.168.11.ci.1 | $260$ | $14$ | $14$ | $11$ |
280.24.1.gs.2 | $280$ | $2$ | $2$ | $1$ |
280.24.1.gv.1 | $280$ | $2$ | $2$ | $1$ |
280.24.1.he.2 | $280$ | $2$ | $2$ | $1$ |
280.24.1.hh.2 | $280$ | $2$ | $2$ | $1$ |