# Properties

 Label 40560.cg Number of curves $4$ Conductor $40560$ CM no Rank $0$ Graph

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cg1")

sage: E.isogeny_class()

## Elliptic curves in class 40560.cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40560.cg1 40560t4 $$[0, 1, 0, -1406136, -642253260]$$ $$31103978031362/195$$ $$1927634442240$$ $$[2]$$ $$516096$$ $$1.9629$$
40560.cg2 40560t3 $$[0, 1, 0, -121736, -1648620]$$ $$20183398562/11567205$$ $$114345347479234560$$ $$[2]$$ $$516096$$ $$1.9629$$
40560.cg3 40560t2 $$[0, 1, 0, -87936, -10044540]$$ $$15214885924/38025$$ $$187944358118400$$ $$[2, 2]$$ $$258048$$ $$1.6163$$
40560.cg4 40560t1 $$[0, 1, 0, -3436, -276340]$$ $$-3631696/24375$$ $$-30119288160000$$ $$[2]$$ $$129024$$ $$1.2697$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 40560.cg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 40560.cg do not have complex multiplication.

## Modular form 40560.2.a.cg

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 4q^{7} + q^{9} + 4q^{11} - q^{15} + 6q^{17} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.