# Properties

 Label 229320.dw Number of curves $2$ Conductor $229320$ CM no Rank $2$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 229320.dw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.dw1 229320j2 $$[0, 0, 0, -214347, 27960086]$$ $$4253577358972/1142578125$$ $$292554990000000000$$ $$$$ $$2457600$$ $$2.0596$$
229320.dw2 229320j1 $$[0, 0, 0, -197967, 33899474]$$ $$13404187799728/1584375$$ $$101419063200000$$ $$$$ $$1228800$$ $$1.7131$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 229320.dw have rank $$2$$.

## Complex multiplication

The elliptic curves in class 229320.dw do not have complex multiplication.

## Modular form 229320.2.a.dw

sage: E.q_eigenform(10)

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