Invariants
Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $320$ | ||
Index: | $1152$ | $\PSL_2$-index: | $576$ | ||||
Genus: | $33 = 1 + \frac{ 576 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 32 }{2}$ | ||||||
Cusps: | $32$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}\cdot20^{8}\cdot40^{8}$ | Cusp orbits | $2^{16}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $2$ | ||||||
$\Q$-gonality: | $7 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $7 \le \gamma \le 12$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.1152.33.4462 |
Level structure
$\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}7&24\\0&39\end{bmatrix}$, $\begin{bmatrix}23&30\\0&27\end{bmatrix}$, $\begin{bmatrix}31&10\\0&11\end{bmatrix}$, $\begin{bmatrix}31&30\\0&9\end{bmatrix}$ |
$\GL_2(\Z/40\Z)$-subgroup: | $D_{20}:C_4^2$ |
Contains $-I$: | no $\quad$ (see 40.576.33.mn.1 for the level structure with $-I$) |
Cyclic 40-isogeny field degree: | $1$ |
Cyclic 40-torsion field degree: | $8$ |
Full 40-torsion field degree: | $640$ |
Jacobian
Conductor: | $2^{136}\cdot5^{31}$ |
Simple: | no |
Squarefree: | no |
Decomposition: | $1^{15}\cdot2\cdot4^{4}$ |
Newforms: | 20.2.a.a$^{3}$, 40.2.a.a$^{2}$, 40.2.d.a$^{3}$, 64.2.a.a$^{2}$, 80.2.a.a, 80.2.a.b, 160.2.d.a, 320.2.a.a, 320.2.a.b, 320.2.a.c, 320.2.a.d, 320.2.a.e, 320.2.a.f, 320.2.a.g |
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
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.192.1-8.j.2.3 | $40$ | $6$ | $6$ | $1$ | $0$ | $1^{14}\cdot2\cdot4^{4}$ |
40.576.15-40.o.2.11 | $40$ | $2$ | $2$ | $15$ | $2$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.15-40.o.2.23 | $40$ | $2$ | $2$ | $15$ | $2$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.15-40.r.1.11 | $40$ | $2$ | $2$ | $15$ | $2$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.15-40.r.1.27 | $40$ | $2$ | $2$ | $15$ | $2$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.15-40.dw.1.14 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.15-40.dw.1.31 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.15-40.dz.1.11 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.15-40.dz.1.18 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{8}\cdot2\cdot4^{2}$ |
40.576.17-40.cu.2.8 | $40$ | $2$ | $2$ | $17$ | $0$ | $1^{8}\cdot4^{2}$ |
40.576.17-40.cu.2.20 | $40$ | $2$ | $2$ | $17$ | $0$ | $1^{8}\cdot4^{2}$ |
40.576.17-40.cx.1.7 | $40$ | $2$ | $2$ | $17$ | $0$ | $1^{8}\cdot4^{2}$ |
40.576.17-40.cx.1.32 | $40$ | $2$ | $2$ | $17$ | $0$ | $1^{8}\cdot4^{2}$ |
40.576.17-40.df.1.19 | $40$ | $2$ | $2$ | $17$ | $2$ | $4^{4}$ |
40.576.17-40.df.1.23 | $40$ | $2$ | $2$ | $17$ | $2$ | $4^{4}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.2304.65-40.pl.3.15 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.2304.65-40.pl.4.14 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.2304.65-40.qh.3.7 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.2304.65-40.qh.4.6 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.2304.65-40.xr.1.5 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.2304.65-40.xr.2.2 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.2304.65-40.yd.1.6 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.2304.65-40.yd.2.4 | $40$ | $2$ | $2$ | $65$ | $2$ | $2^{6}\cdot4^{5}$ |
40.5760.193-40.sl.1.1 | $40$ | $5$ | $5$ | $193$ | $27$ | $1^{68}\cdot2^{22}\cdot4^{12}$ |