# Properties

 Label 229320.du Number of curves $2$ Conductor $229320$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("du1")

sage: E.isogeny_class()

## Elliptic curves in class 229320.du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.du1 229320cz2 $$[0, 0, 0, -141267, -20140274]$$ $$1775007362/29575$$ $$5194819642521600$$ $$$$ $$1474560$$ $$1.8140$$
229320.du2 229320cz1 $$[0, 0, 0, -17787, 431494]$$ $$7086244/3185$$ $$279721057674240$$ $$$$ $$737280$$ $$1.4674$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 229320.du have rank $$1$$.

## Complex multiplication

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

## Modular form 229320.2.a.du

sage: E.q_eigenform(10)

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