# Properties

 Label 229320du 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 229320du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.z1 229320du1 $$[0, 0, 0, -8668443, -4624536602]$$ $$820221748268836/369468094905$$ $$32448353621259994629120$$ $$[2]$$ $$14450688$$ $$3.0148$$ $$\Gamma_0(N)$$-optimal
229320.z2 229320du2 $$[0, 0, 0, 30086637, -34628719538]$$ $$17147425715207422/12872524043925$$ $$-2261046179280242411366400$$ $$[2]$$ $$28901376$$ $$3.3613$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 229320.2.a.du

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.