Invariants
Level: | $40$ | $\SL_2$-level: | $8$ | ||||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 4 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $4$ 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: | 8H0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.24.0.335 |
Level structure
$\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}3&32\\2&19\end{bmatrix}$, $\begin{bmatrix}15&38\\36&33\end{bmatrix}$, $\begin{bmatrix}31&26\\30&1\end{bmatrix}$, $\begin{bmatrix}37&22\\15&31\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 40-isogeny field degree: | $24$ |
Cyclic 40-torsion field degree: | $384$ |
Full 40-torsion field degree: | $30720$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 5 x^{2} + 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.
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This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.12.0.q.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
20.12.0.n.1 | $20$ | $2$ | $2$ | $0$ | $0$ |
40.12.0.cb.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
40.48.1.bk.1 | $40$ | $2$ | $2$ | $1$ |
40.48.1.cj.1 | $40$ | $2$ | $2$ | $1$ |
40.48.1.cv.1 | $40$ | $2$ | $2$ | $1$ |
40.48.1.db.1 | $40$ | $2$ | $2$ | $1$ |
40.48.1.eu.1 | $40$ | $2$ | $2$ | $1$ |
40.48.1.fg.1 | $40$ | $2$ | $2$ | $1$ |
40.48.1.fl.1 | $40$ | $2$ | $2$ | $1$ |
40.48.1.fx.1 | $40$ | $2$ | $2$ | $1$ |
40.120.8.eo.1 | $40$ | $5$ | $5$ | $8$ |
40.144.7.nu.1 | $40$ | $6$ | $6$ | $7$ |
40.240.15.xc.1 | $40$ | $10$ | $10$ | $15$ |
120.48.1.bly.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bmg.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bmo.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bmw.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bqw.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bre.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.brn.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.brv.1 | $120$ | $2$ | $2$ | $1$ |
120.72.2.sg.1 | $120$ | $3$ | $3$ | $2$ |
120.96.5.zg.1 | $120$ | $4$ | $4$ | $5$ |
280.48.1.bus.1 | $280$ | $2$ | $2$ | $1$ |
280.48.1.buw.1 | $280$ | $2$ | $2$ | $1$ |
280.48.1.bvi.1 | $280$ | $2$ | $2$ | $1$ |
280.48.1.bvm.1 | $280$ | $2$ | $2$ | $1$ |
280.48.1.bzq.1 | $280$ | $2$ | $2$ | $1$ |
280.48.1.bzu.1 | $280$ | $2$ | $2$ | $1$ |
280.48.1.cag.1 | $280$ | $2$ | $2$ | $1$ |
280.48.1.cak.1 | $280$ | $2$ | $2$ | $1$ |
280.192.13.ya.1 | $280$ | $8$ | $8$ | $13$ |