Invariants
Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $1600$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{2}\cdot40^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $2$ | ||||||
$\Q$-gonality: | $5 \le \gamma \le 10$ | ||||||
$\overline{\Q}$-gonality: | $5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40B16 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.480.16.887 |
Level structure
$\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}9&8\\4&21\end{bmatrix}$, $\begin{bmatrix}17&16\\26&15\end{bmatrix}$, $\begin{bmatrix}17&20\\16&31\end{bmatrix}$, $\begin{bmatrix}23&36\\18&29\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 40.240.16.z.2 for the level structure with $-I$) |
Cyclic 40-isogeny field degree: | $12$ |
Cyclic 40-torsion field degree: | $192$ |
Full 40-torsion field degree: | $1536$ |
Jacobian
Conductor: | $2^{54}\cdot5^{32}$ |
Simple: | no |
Squarefree: | no |
Decomposition: | $1^{8}\cdot2^{4}$ |
Newforms: | 50.2.a.b$^{3}$, 200.2.a.e, 200.2.d.a, 200.2.d.b, 200.2.d.c, 200.2.d.d, 1600.2.a.b, 1600.2.a.j, 1600.2.a.p, 1600.2.a.x |
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 |
---|---|---|---|---|---|---|
40.96.0-40.t.1.11 | $40$ | $5$ | $5$ | $0$ | $0$ | full Jacobian |
40.240.8-40.m.2.15 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
40.240.8-40.m.2.27 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
40.240.8-40.n.2.12 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
40.240.8-40.n.2.28 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
40.240.8-40.q.1.3 | $40$ | $2$ | $2$ | $8$ | $2$ | $2^{4}$ |
40.240.8-40.q.1.19 | $40$ | $2$ | $2$ | $8$ | $2$ | $2^{4}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.960.33-40.co.1.1 | $40$ | $2$ | $2$ | $33$ | $7$ | $1^{7}\cdot2^{5}$ |
40.960.33-40.cr.1.2 | $40$ | $2$ | $2$ | $33$ | $7$ | $1^{7}\cdot2^{5}$ |
40.960.33-40.cu.2.2 | $40$ | $2$ | $2$ | $33$ | $5$ | $1^{7}\cdot2^{5}$ |
40.960.33-40.cy.2.5 | $40$ | $2$ | $2$ | $33$ | $5$ | $1^{7}\cdot2^{5}$ |
40.960.33-40.de.2.1 | $40$ | $2$ | $2$ | $33$ | $7$ | $1^{7}\cdot2^{5}$ |
40.960.33-40.df.2.6 | $40$ | $2$ | $2$ | $33$ | $8$ | $1^{7}\cdot2^{5}$ |
40.960.33-40.dg.1.3 | $40$ | $2$ | $2$ | $33$ | $5$ | $1^{7}\cdot2^{5}$ |
40.960.33-40.dh.1.1 | $40$ | $2$ | $2$ | $33$ | $6$ | $1^{7}\cdot2^{5}$ |
40.1440.46-40.ep.2.28 | $40$ | $3$ | $3$ | $46$ | $6$ | $1^{14}\cdot4^{4}$ |
40.1920.61-40.hr.2.14 | $40$ | $4$ | $4$ | $61$ | $9$ | $1^{21}\cdot2^{4}\cdot4^{4}$ |