Invariants
Level: | $20$ | $\SL_2$-level: | $10$ | ||||
Index: | $36$ | $\PSL_2$-index: | $36$ | ||||
Genus: | $0 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $1^{2}\cdot2^{2}\cdot5^{2}\cdot10^{2}$ | Cusp orbits | $2^{4}$ | ||
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: | 10F0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 20.36.0.7 |
Level structure
$\GL_2(\Z/20\Z)$-generators: | $\begin{bmatrix}1&6\\4&1\end{bmatrix}$, $\begin{bmatrix}3&19\\10&11\end{bmatrix}$, $\begin{bmatrix}7&5\\0&17\end{bmatrix}$, $\begin{bmatrix}11&13\\0&7\end{bmatrix}$ |
$\GL_2(\Z/20\Z)$-subgroup: | $C_2^3.D_4\times F_5$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 20-isogeny field degree: | $2$ |
Cyclic 20-torsion field degree: | $16$ |
Full 20-torsion field degree: | $1280$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 5 x^{2} + 20 x y + 40 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 |
---|---|---|---|---|---|
$X_0(10)$ | $10$ | $2$ | $2$ | $0$ | $0$ |
20.12.0.m.2 | $20$ | $3$ | $3$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
20.72.1.a.1 | $20$ | $2$ | $2$ | $1$ |
20.72.1.c.1 | $20$ | $2$ | $2$ | $1$ |
20.72.1.e.1 | $20$ | $2$ | $2$ | $1$ |
20.72.1.g.1 | $20$ | $2$ | $2$ | $1$ |
20.72.1.h.2 | $20$ | $2$ | $2$ | $1$ |
20.72.1.j.2 | $20$ | $2$ | $2$ | $1$ |
20.72.1.l.1 | $20$ | $2$ | $2$ | $1$ |
20.72.1.n.1 | $20$ | $2$ | $2$ | $1$ |
20.72.3.bh.1 | $20$ | $2$ | $2$ | $3$ |
20.72.3.bj.1 | $20$ | $2$ | $2$ | $3$ |
20.72.3.bl.1 | $20$ | $2$ | $2$ | $3$ |
20.72.3.bn.1 | $20$ | $2$ | $2$ | $3$ |
20.180.4.a.1 | $20$ | $5$ | $5$ | $4$ |
40.72.1.d.2 | $40$ | $2$ | $2$ | $1$ |
40.72.1.k.1 | $40$ | $2$ | $2$ | $1$ |
40.72.1.q.1 | $40$ | $2$ | $2$ | $1$ |
40.72.1.w.1 | $40$ | $2$ | $2$ | $1$ |
40.72.1.bb.2 | $40$ | $2$ | $2$ | $1$ |
40.72.1.bi.2 | $40$ | $2$ | $2$ | $1$ |
40.72.1.bo.1 | $40$ | $2$ | $2$ | $1$ |
40.72.1.bu.2 | $40$ | $2$ | $2$ | $1$ |
40.72.3.eh.1 | $40$ | $2$ | $2$ | $3$ |
40.72.3.en.1 | $40$ | $2$ | $2$ | $3$ |
40.72.3.et.2 | $40$ | $2$ | $2$ | $3$ |
40.72.3.ez.1 | $40$ | $2$ | $2$ | $3$ |
60.72.1.v.1 | $60$ | $2$ | $2$ | $1$ |
60.72.1.x.1 | $60$ | $2$ | $2$ | $1$ |
60.72.1.z.1 | $60$ | $2$ | $2$ | $1$ |
60.72.1.bb.1 | $60$ | $2$ | $2$ | $1$ |
60.72.1.ce.2 | $60$ | $2$ | $2$ | $1$ |
60.72.1.cg.2 | $60$ | $2$ | $2$ | $1$ |
60.72.1.ci.1 | $60$ | $2$ | $2$ | $1$ |
60.72.1.ck.1 | $60$ | $2$ | $2$ | $1$ |
60.72.3.xv.1 | $60$ | $2$ | $2$ | $3$ |
60.72.3.xx.1 | $60$ | $2$ | $2$ | $3$ |
60.72.3.yt.1 | $60$ | $2$ | $2$ | $3$ |
60.72.3.yv.1 | $60$ | $2$ | $2$ | $3$ |
60.108.6.a.1 | $60$ | $3$ | $3$ | $6$ |
60.144.5.oc.1 | $60$ | $4$ | $4$ | $5$ |
100.180.4.a.1 | $100$ | $5$ | $5$ | $4$ |
120.72.1.cy.2 | $120$ | $2$ | $2$ | $1$ |
120.72.1.de.1 | $120$ | $2$ | $2$ | $1$ |
120.72.1.dk.1 | $120$ | $2$ | $2$ | $1$ |
120.72.1.dq.1 | $120$ | $2$ | $2$ | $1$ |
120.72.1.ho.2 | $120$ | $2$ | $2$ | $1$ |
120.72.1.hu.2 | $120$ | $2$ | $2$ | $1$ |
120.72.1.ia.1 | $120$ | $2$ | $2$ | $1$ |
120.72.1.ig.2 | $120$ | $2$ | $2$ | $1$ |
120.72.3.fsh.1 | $120$ | $2$ | $2$ | $3$ |
120.72.3.fsn.1 | $120$ | $2$ | $2$ | $3$ |
120.72.3.fvn.2 | $120$ | $2$ | $2$ | $3$ |
120.72.3.fvt.1 | $120$ | $2$ | $2$ | $3$ |
140.72.1.r.1 | $140$ | $2$ | $2$ | $1$ |
140.72.1.s.1 | $140$ | $2$ | $2$ | $1$ |
140.72.1.v.1 | $140$ | $2$ | $2$ | $1$ |
140.72.1.w.1 | $140$ | $2$ | $2$ | $1$ |
140.72.1.y.2 | $140$ | $2$ | $2$ | $1$ |
140.72.1.z.2 | $140$ | $2$ | $2$ | $1$ |
140.72.1.bc.1 | $140$ | $2$ | $2$ | $1$ |
140.72.1.bd.1 | $140$ | $2$ | $2$ | $1$ |
140.72.3.co.1 | $140$ | $2$ | $2$ | $3$ |
140.72.3.cp.1 | $140$ | $2$ | $2$ | $3$ |
140.72.3.cw.1 | $140$ | $2$ | $2$ | $3$ |
140.72.3.cx.1 | $140$ | $2$ | $2$ | $3$ |
140.288.17.a.2 | $140$ | $8$ | $8$ | $17$ |
220.72.1.p.2 | $220$ | $2$ | $2$ | $1$ |
220.72.1.q.2 | $220$ | $2$ | $2$ | $1$ |
220.72.1.t.1 | $220$ | $2$ | $2$ | $1$ |
220.72.1.u.1 | $220$ | $2$ | $2$ | $1$ |
220.72.1.w.2 | $220$ | $2$ | $2$ | $1$ |
220.72.1.x.2 | $220$ | $2$ | $2$ | $1$ |
220.72.1.ba.1 | $220$ | $2$ | $2$ | $1$ |
220.72.1.bb.1 | $220$ | $2$ | $2$ | $1$ |
220.72.3.co.1 | $220$ | $2$ | $2$ | $3$ |
220.72.3.cp.1 | $220$ | $2$ | $2$ | $3$ |
220.72.3.cw.1 | $220$ | $2$ | $2$ | $3$ |
220.72.3.cx.1 | $220$ | $2$ | $2$ | $3$ |
260.72.1.r.2 | $260$ | $2$ | $2$ | $1$ |
260.72.1.s.2 | $260$ | $2$ | $2$ | $1$ |
260.72.1.v.1 | $260$ | $2$ | $2$ | $1$ |
260.72.1.w.1 | $260$ | $2$ | $2$ | $1$ |
260.72.1.y.1 | $260$ | $2$ | $2$ | $1$ |
260.72.1.z.1 | $260$ | $2$ | $2$ | $1$ |
260.72.1.bc.1 | $260$ | $2$ | $2$ | $1$ |
260.72.1.bd.1 | $260$ | $2$ | $2$ | $1$ |
260.72.3.co.1 | $260$ | $2$ | $2$ | $3$ |
260.72.3.cp.1 | $260$ | $2$ | $2$ | $3$ |
260.72.3.cw.1 | $260$ | $2$ | $2$ | $3$ |
260.72.3.cx.1 | $260$ | $2$ | $2$ | $3$ |
280.72.1.cg.2 | $280$ | $2$ | $2$ | $1$ |
280.72.1.cj.1 | $280$ | $2$ | $2$ | $1$ |
280.72.1.cs.1 | $280$ | $2$ | $2$ | $1$ |
280.72.1.cv.1 | $280$ | $2$ | $2$ | $1$ |
280.72.1.de.2 | $280$ | $2$ | $2$ | $1$ |
280.72.1.dh.2 | $280$ | $2$ | $2$ | $1$ |
280.72.1.dq.1 | $280$ | $2$ | $2$ | $1$ |
280.72.1.dt.2 | $280$ | $2$ | $2$ | $1$ |
280.72.3.ic.1 | $280$ | $2$ | $2$ | $3$ |
280.72.3.if.1 | $280$ | $2$ | $2$ | $3$ |
280.72.3.ja.2 | $280$ | $2$ | $2$ | $3$ |
280.72.3.jd.1 | $280$ | $2$ | $2$ | $3$ |