# Properties

 Label 4560.k Number of curves $4$ Conductor $4560$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.k1 4560u3 $$[0, -1, 0, -48640, -4112768]$$ $$3107086841064961/570$$ $$2334720$$ $$[2]$$ $$9216$$ $$1.0577$$
4560.k2 4560u4 $$[0, -1, 0, -3520, -41600]$$ $$1177918188481/488703750$$ $$2001730560000$$ $$[4]$$ $$9216$$ $$1.0577$$
4560.k3 4560u2 $$[0, -1, 0, -3040, -63488]$$ $$758800078561/324900$$ $$1330790400$$ $$[2, 2]$$ $$4608$$ $$0.71109$$
4560.k4 4560u1 $$[0, -1, 0, -160, -1280]$$ $$-111284641/123120$$ $$-504299520$$ $$[2]$$ $$2304$$ $$0.36452$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4560.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4560.k do not have complex multiplication.

## Modular form4560.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 4 q^{7} + q^{9} + 4 q^{11} - 2 q^{13} - q^{15} - 2 q^{17} + q^{19} + O(q^{20})$$

## 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 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.