# Properties

 Label 229320bf Number of curves $4$ Conductor $229320$ CM no Rank $2$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 229320bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.i3 229320bf1 $$[0, 0, 0, -49098, 4177397]$$ $$9538484224/26325$$ $$36124690165200$$ $$[2]$$ $$884736$$ $$1.4744$$ $$\Gamma_0(N)$$-optimal
229320.i2 229320bf2 $$[0, 0, 0, -68943, 482258]$$ $$1650587344/950625$$ $$20872043206560000$$ $$[2, 2]$$ $$1769472$$ $$1.8210$$
229320.i4 229320bf3 $$[0, 0, 0, 275037, 3853262]$$ $$26198797244/15234375$$ $$-1337951487600000000$$ $$[2]$$ $$3538944$$ $$2.1676$$
229320.i1 229320bf4 $$[0, 0, 0, -730443, -239377642]$$ $$490757540836/2142075$$ $$188126682768460800$$ $$[2]$$ $$3538944$$ $$2.1676$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 229320.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{11} - q^{13} - 6q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.