# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("dr1")

sage: E.isogeny_class()

## Elliptic curves in class 229320dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.o2 229320dr1 $$[0, 0, 0, -187383, 29634122]$$ $$11367178023472/651619215$$ $$41711470042394880$$ $$$$ $$1916928$$ $$1.9433$$ $$\Gamma_0(N)$$-optimal
229320.o1 229320dr2 $$[0, 0, 0, -2955603, 1955761598]$$ $$11151682683009628/40040325$$ $$10252250260761600$$ $$$$ $$3833856$$ $$2.2899$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 229320.2.a.dr

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{11} + q^{13} + 2q^{19} + O(q^{20})$$ ## 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. 