# Properties

 Label 44352.dw Number of curves $4$ Conductor $44352$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dw1")

sage: E.isogeny_class()

## Elliptic curves in class 44352.dw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44352.dw1 44352dl4 $$[0, 0, 0, -23048364, -30199120432]$$ $$14171198121996897746/4077720290568771$$ $$389632241411638435381248$$ $$$$ $$5898240$$ $$3.2330$$
44352.dw2 44352dl2 $$[0, 0, 0, -21131724, -37384987120]$$ $$21843440425782779332/3100814593569$$ $$148143724213816590336$$ $$[2, 2]$$ $$2949120$$ $$2.8864$$
44352.dw3 44352dl1 $$[0, 0, 0, -21131004, -37387662352]$$ $$87364831012240243408/1760913$$ $$21032232173568$$ $$$$ $$1474560$$ $$2.5399$$ $$\Gamma_0(N)$$-optimal
44352.dw4 44352dl3 $$[0, 0, 0, -19226604, -44399638960]$$ $$-8226100326647904626/4152140742401883$$ $$-396743226321924614651904$$ $$$$ $$5898240$$ $$3.2330$$

## Rank

sage: E.rank()

The elliptic curves in class 44352.dw have rank $$1$$.

## Complex multiplication

The elliptic curves in class 44352.dw do not have complex multiplication.

## Modular form 44352.2.a.dw

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. 