# Properties

 Label 5544.f Number of curves $2$ Conductor $5544$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 5544.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5544.f1 5544n1 $$[0, 0, 0, -531, -4706]$$ $$598885164/539$$ $$14902272$$ $$$$ $$1792$$ $$0.30083$$ $$\Gamma_0(N)$$-optimal
5544.f2 5544n2 $$[0, 0, 0, -411, -6890]$$ $$-138853062/290521$$ $$-16064649216$$ $$$$ $$3584$$ $$0.64740$$

## Rank

sage: E.rank()

The elliptic curves in class 5544.f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5544.f do not have complex multiplication.

## Modular form5544.2.a.f

sage: E.q_eigenform(10)

$$q - 2 q^{5} + q^{7} + q^{11} + 4 q^{13} + 6 q^{17} + 2 q^{19} + O(q^{20})$$ ## 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. 