# Properties

 Label 5544.c Number of curves $4$ Conductor $5544$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 5544.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5544.c1 5544t3 $$[0, 0, 0, -5762091, 3774890054]$$ $$14171198121996897746/4077720290568771$$ $$6088003772056850552832$$ $$$$ $$368640$$ $$2.8864$$
5544.c2 5544t2 $$[0, 0, 0, -5282931, 4673123390]$$ $$21843440425782779332/3100814593569$$ $$2314745690840884224$$ $$[2, 2]$$ $$184320$$ $$2.5399$$
5544.c3 5544t1 $$[0, 0, 0, -5282751, 4673457794]$$ $$87364831012240243408/1760913$$ $$328628627712$$ $$$$ $$92160$$ $$2.1933$$ $$\Gamma_0(N)$$-optimal
5544.c4 5544t4 $$[0, 0, 0, -4806651, 5549954870]$$ $$-8226100326647904626/4152140742401883$$ $$-6199112911280072103936$$ $$$$ $$368640$$ $$2.8864$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5544.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - q^{11} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 