# Properties

 Label 4560.r Number of curves $2$ Conductor $4560$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.r1 4560z2 $$[0, 1, 0, -25896, -1612620]$$ $$468898230633769/5540400$$ $$22693478400$$ $$$$ $$9216$$ $$1.1371$$
4560.r2 4560z1 $$[0, 1, 0, -1576, -26956]$$ $$-105756712489/12476160$$ $$-51102351360$$ $$$$ $$4608$$ $$0.79056$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.r

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 