Invariants
| Level: | $40$ | $\SL_2$-level: | $8$ | Newform level: | $1600$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8K1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.192.1.232 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}3&14\\0&9\end{bmatrix}$, $\begin{bmatrix}11&16\\8&17\end{bmatrix}$, $\begin{bmatrix}31&12\\16&9\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 40.96.1.ch.1 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $6$ |
| Cyclic 40-torsion field degree: | $96$ |
| Full 40-torsion field degree: | $3840$ |
Jacobian
| Conductor: | $2^{6}\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 1600.2.a.n |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.96.0-8.l.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.0-8.l.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.0-40.o.2.7 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.0-40.o.2.15 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.0-40.p.2.1 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.0-40.p.2.10 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.0-40.bc.2.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.0-40.bc.2.15 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.96.1-40.bi.2.9 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 40.96.1-40.bi.2.15 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 40.96.1-40.bj.2.5 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 40.96.1-40.bj.2.7 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 40.96.1-40.bv.1.3 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 40.96.1-40.bv.1.8 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
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.ll.2.1 | $40$ | $5$ | $5$ | $33$ | $5$ | $1^{14}\cdot2^{9}$ |
| 40.1152.33-40.wr.2.9 | $40$ | $6$ | $6$ | $33$ | $4$ | $1^{14}\cdot2\cdot4^{4}$ |
| 40.1920.65-40.bhj.1.3 | $40$ | $10$ | $10$ | $65$ | $8$ | $1^{28}\cdot2^{10}\cdot4^{4}$ |
| 80.384.5-80.dd.1.4 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.eb.1.3 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.gb.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.gc.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.gj.1.2 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.gk.1.3 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.gv.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.gw.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.hd.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.he.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.hm.1.3 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 80.384.5-80.hu.1.1 | $80$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.tg.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.ue.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.zn.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.zo.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.zv.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.zw.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.bah.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.bai.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.bap.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.baq.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.beh.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.bff.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |