Invariants
Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $1600$ | ||
Index: | $480$ | $\PSL_2$-index: | $480$ | ||||
Genus: | $29 = 1 + \frac{ 480 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $10^{16}\cdot40^{8}$ | Cusp orbits | $8^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $21$ | ||||||
$\Q$-gonality: | $8 \le \gamma \le 16$ | ||||||
$\overline{\Q}$-gonality: | $8 \le \gamma \le 16$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.480.29.205 |
Level structure
$\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}1&12\\34&21\end{bmatrix}$, $\begin{bmatrix}23&12\\1&17\end{bmatrix}$, $\begin{bmatrix}23&28\\19&17\end{bmatrix}$, $\begin{bmatrix}31&0\\20&31\end{bmatrix}$, $\begin{bmatrix}37&32\\21&3\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 40.960.29-40.tj.1.1, 40.960.29-40.tj.1.2, 40.960.29-40.tj.1.3, 40.960.29-40.tj.1.4, 40.960.29-40.tj.1.5, 40.960.29-40.tj.1.6, 40.960.29-40.tj.1.7, 40.960.29-40.tj.1.8 |
Cyclic 40-isogeny field degree: | $12$ |
Cyclic 40-torsion field degree: | $192$ |
Full 40-torsion field degree: | $1536$ |
Jacobian
Conductor: | $2^{134}\cdot5^{58}$ |
Simple: | no |
Squarefree: | no |
Decomposition: | $1^{29}$ |
Newforms: | 50.2.a.a, 50.2.a.b$^{2}$, 100.2.a.a, 200.2.a.a, 200.2.a.b, 200.2.a.d, 400.2.a.a, 400.2.a.c, 400.2.a.d$^{2}$, 400.2.a.e, 400.2.a.f, 1600.2.a.a$^{2}$, 1600.2.a.b$^{2}$, 1600.2.a.c$^{2}$, 1600.2.a.d$^{2}$, 1600.2.a.o$^{2}$, 1600.2.a.p$^{2}$, 1600.2.a.q$^{2}$, 1600.2.a.u$^{2}$ |
Rational points
This modular curve has no $\Q_p$ points for $p=17,89$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
20.240.13.bf.1 | $20$ | $2$ | $2$ | $13$ | $5$ | $1^{16}$ |
40.240.13.ob.1 | $40$ | $2$ | $2$ | $13$ | $10$ | $1^{16}$ |
40.240.13.yb.1 | $40$ | $2$ | $2$ | $13$ | $11$ | $1^{16}$ |
40.240.15.et.1 | $40$ | $2$ | $2$ | $15$ | $10$ | $1^{14}$ |
40.240.15.fd.1 | $40$ | $2$ | $2$ | $15$ | $10$ | $1^{14}$ |
40.240.15.jj.1 | $40$ | $2$ | $2$ | $15$ | $9$ | $1^{14}$ |
40.240.15.pt.1 | $40$ | $2$ | $2$ | $15$ | $12$ | $1^{14}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.960.65.cum.1 | $40$ | $2$ | $2$ | $65$ | $33$ | $1^{26}\cdot2^{5}$ |
40.960.65.cun.1 | $40$ | $2$ | $2$ | $65$ | $36$ | $1^{26}\cdot2^{5}$ |
40.960.65.cuo.1 | $40$ | $2$ | $2$ | $65$ | $30$ | $1^{26}\cdot2^{5}$ |
40.960.65.cup.1 | $40$ | $2$ | $2$ | $65$ | $36$ | $1^{26}\cdot2^{5}$ |
40.1440.85.wp.1 | $40$ | $3$ | $3$ | $85$ | $40$ | $1^{56}$ |