# Properties

 Label 40560ct Number of curves $2$ Conductor $40560$ CM no Rank $0$ Graph

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 40560ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40560.cw2 40560ct1 $$[0, 1, 0, 10760, 1195988]$$ $$6967871/35100$$ $$-693948399206400$$ $$[2]$$ $$193536$$ $$1.5300$$ $$\Gamma_0(N)$$-optimal
40560.cw1 40560ct2 $$[0, 1, 0, -124440, 15094548]$$ $$10779215329/1232010$$ $$24357588812144640$$ $$[2]$$ $$387072$$ $$1.8766$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 40560.2.a.ct

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 2q^{7} + q^{9} + 4q^{11} + q^{15} + 8q^{17} - 6q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.