# Properties

 Label 705600.bwy Number of curves $2$ Conductor $705600$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bwy1")

sage: E.isogeny_class()

## Elliptic curves in class 705600.bwy

sage: E.isogeny_class().curves

LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bwy1 $$[0, 0, 0, -216300, -27538000]$$ $$2185454/625$$ $$320060160000000000$$ $$$$ $$7077888$$ $$2.0655$$
705600.bwy2 $$[0, 0, 0, 35700, -2842000]$$ $$19652/25$$ $$-6401203200000000$$ $$$$ $$3538944$$ $$1.7189$$

## Rank

sage: E.rank()

The elliptic curves in class 705600.bwy have rank $$1$$.

## Complex multiplication

The elliptic curves in class 705600.bwy do not have complex multiplication.

## Modular form 705600.2.a.bwy

sage: E.q_eigenform(10)

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

## 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. 