# Properties

 Label 70560bw Number of curves $4$ Conductor $70560$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

## Elliptic curves in class 70560bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70560.ci3 70560bw1 $$[0, 0, 0, -31017, 2068976]$$ $$601211584/11025$$ $$60516574977600$$ $$[2, 2]$$ $$294912$$ $$1.4393$$ $$\Gamma_0(N)$$-optimal
70560.ci4 70560bw2 $$[0, 0, 0, -147, 6001814]$$ $$-8/354375$$ $$-15561404994240000$$ $$$$ $$589824$$ $$1.7858$$
70560.ci2 70560bw3 $$[0, 0, 0, -64092, -3117184]$$ $$82881856/36015$$ $$12651998608650240$$ $$$$ $$589824$$ $$1.7858$$
70560.ci1 70560bw4 $$[0, 0, 0, -494067, 133667786]$$ $$303735479048/105$$ $$4610786664960$$ $$$$ $$589824$$ $$1.7858$$

## Rank

sage: E.rank()

The elliptic curves in class 70560bw have rank $$2$$.

## Complex multiplication

The elliptic curves in class 70560bw do not have complex multiplication.

## Modular form 70560.2.a.bw

sage: E.q_eigenform(10)

$$q + q^{5} - 4q^{11} - 6q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 