↑

Properties

Label 40.96.1.t.1
Level $40$
Index $96$
Genus $1$
Analytic rank $0$
Cusps $16$
$\Q$-cusps $0$

Related objects

Downloads

Learn more

Invariants

Level: $40$ $\SL_2$-level: $8$ Newform level: $32$
Index: $96$ $\PSL_2$-index:$96$
Genus: $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$
Cusps: $16$ (none of which are rational) Cusp widths $4^{8}\cdot8^{8}$ Cusp orbits $2^{2}\cdot4^{3}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $0$
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 8K1
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 40.96.1.866

Level structure

$\GL_2(\Z/40\Z)$-generators: $\begin{bmatrix}1&0\\14&39\end{bmatrix}$, $\begin{bmatrix}19&32\\16&39\end{bmatrix}$, $\begin{bmatrix}25&36\\2&5\end{bmatrix}$, $\begin{bmatrix}31&12\\16&29\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 40.192.1-40.t.1.1, 40.192.1-40.t.1.2, 40.192.1-40.t.1.3, 40.192.1-40.t.1.4, 40.192.1-40.t.1.5, 40.192.1-40.t.1.6, 40.192.1-40.t.1.7, 40.192.1-40.t.1.8, 80.192.1-40.t.1.1, 80.192.1-40.t.1.2, 80.192.1-40.t.1.3, 80.192.1-40.t.1.4, 80.192.1-40.t.1.5, 80.192.1-40.t.1.6, 80.192.1-40.t.1.7, 80.192.1-40.t.1.8, 80.192.1-40.t.1.9, 80.192.1-40.t.1.10, 80.192.1-40.t.1.11, 80.192.1-40.t.1.12, 120.192.1-40.t.1.1, 120.192.1-40.t.1.2, 120.192.1-40.t.1.3, 120.192.1-40.t.1.4, 120.192.1-40.t.1.5, 120.192.1-40.t.1.6, 120.192.1-40.t.1.7, 120.192.1-40.t.1.8, 240.192.1-40.t.1.1, 240.192.1-40.t.1.2, 240.192.1-40.t.1.3, 240.192.1-40.t.1.4, 240.192.1-40.t.1.5, 240.192.1-40.t.1.6, 240.192.1-40.t.1.7, 240.192.1-40.t.1.8, 240.192.1-40.t.1.9, 240.192.1-40.t.1.10, 240.192.1-40.t.1.11, 240.192.1-40.t.1.12, 280.192.1-40.t.1.1, 280.192.1-40.t.1.2, 280.192.1-40.t.1.3, 280.192.1-40.t.1.4, 280.192.1-40.t.1.5, 280.192.1-40.t.1.6, 280.192.1-40.t.1.7, 280.192.1-40.t.1.8
Cyclic 40-isogeny field degree: $12$
Cyclic 40-torsion field degree: $96$
Full 40-torsion field degree: $7680$

Jacobian

Conductor: $2^{5}$
Simple: yes
Squarefree: yes
Decomposition: $1$
Newforms: 32.2.a.a

Models

Embedded model Embedded model in $\mathbb{P}^{3}$

$ 0 $ $=$ $ 5 y^{2} - z^{2} - w^{2} $
$=$ $5 x^{2} - z^{2} - 2 w^{2}$
 Copy content Toggle raw display

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Maps to other modular curves

$j$-invariant map of degree 96 from the embedded model of this modular curve to the modular curve $X(1)$ :

$\displaystyle j$ $=$ $\displaystyle 2^8\,\frac{(z^{8}+4z^{6}w^{2}+5z^{4}w^{4}+2z^{2}w^{6}+w^{8})^{3}}{w^{8}z^{4}(z^{2}+w^{2})^{4}(z^{2}+2w^{2})^{2}}$

Modular covers

Sorry, your browser does not support the nearby lattice.

Cover information

Click on a modular curve in the diagram to see information about it.
See a full page version of the diagram

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
8.48.1.i.1 $8$ $2$ $2$ $1$ $0$ dimension zero
40.48.0.j.2 $40$ $2$ $2$ $0$ $0$ full Jacobian
40.48.0.l.1 $40$ $2$ $2$ $0$ $0$ full Jacobian
40.48.0.v.1 $40$ $2$ $2$ $0$ $0$ full Jacobian
40.48.0.x.2 $40$ $2$ $2$ $0$ $0$ full Jacobian
40.48.1.p.1 $40$ $2$ $2$ $1$ $0$ dimension zero
40.48.1.s.2 $40$ $2$ $2$ $1$ $0$ 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
40.480.33.cq.1 $40$ $5$ $5$ $33$ $5$ $1^{14}\cdot2^{9}$
40.576.33.jo.2 $40$ $6$ $6$ $33$ $3$ $1^{14}\cdot2\cdot4^{4}$
40.960.65.ne.1 $40$ $10$ $10$ $65$ $7$ $1^{28}\cdot2^{10}\cdot4^{4}$
80.192.5.o.2 $80$ $2$ $2$ $5$ $?$ not computed
80.192.5.u.2 $80$ $2$ $2$ $5$ $?$ not computed
80.192.5.br.1 $80$ $2$ $2$ $5$ $?$ not computed
80.192.5.bs.1 $80$ $2$ $2$ $5$ $?$ not computed
80.192.5.ei.1 $80$ $2$ $2$ $5$ $?$ not computed
80.192.5.ej.1 $80$ $2$ $2$ $5$ $?$ not computed
80.192.5.ff.2 $80$ $2$ $2$ $5$ $?$ not computed
80.192.5.fl.2 $80$ $2$ $2$ $5$ $?$ not computed
80.192.9.im.2 $80$ $2$ $2$ $9$ $?$ not computed
80.192.9.in.2 $80$ $2$ $2$ $9$ $?$ not computed
80.192.9.iv.2 $80$ $2$ $2$ $9$ $?$ not computed
80.192.9.iw.2 $80$ $2$ $2$ $9$ $?$ not computed
120.288.17.bys.1 $120$ $3$ $3$ $17$ $?$ not computed
120.384.17.sn.2 $120$ $4$ $4$ $17$ $?$ not computed
240.192.5.cc.2 $240$ $2$ $2$ $5$ $?$ not computed
240.192.5.ci.2 $240$ $2$ $2$ $5$ $?$ not computed
240.192.5.et.1 $240$ $2$ $2$ $5$ $?$ not computed
240.192.5.eu.1 $240$ $2$ $2$ $5$ $?$ not computed
240.192.5.ni.1 $240$ $2$ $2$ $5$ $?$ not computed
240.192.5.nj.1 $240$ $2$ $2$ $5$ $?$ not computed
240.192.5.pt.2 $240$ $2$ $2$ $5$ $?$ not computed
240.192.5.pz.2 $240$ $2$ $2$ $5$ $?$ not computed
240.192.9.bfi.1 $240$ $2$ $2$ $9$ $?$ not computed
240.192.9.bfj.1 $240$ $2$ $2$ $9$ $?$ not computed
240.192.9.bfv.1 $240$ $2$ $2$ $9$ $?$ not computed
240.192.9.bfw.1 $240$ $2$ $2$ $9$ $?$ not computed