# Properties

 Label 15680.bw Number of curves $4$ Conductor $15680$ CM no Rank $2$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 15680.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.bw1 15680e3 $$[0, 0, 0, -16268, 773808]$$ $$123505992/4375$$ $$16866160640000$$ $$$$ $$36864$$ $$1.3087$$
15680.bw2 15680e2 $$[0, 0, 0, -2548, -32928]$$ $$3796416/1225$$ $$590315622400$$ $$[2, 2]$$ $$18432$$ $$0.96212$$
15680.bw3 15680e1 $$[0, 0, 0, -2303, -42532]$$ $$179406144/35$$ $$263533760$$ $$$$ $$9216$$ $$0.61555$$ $$\Gamma_0(N)$$-optimal
15680.bw4 15680e4 $$[0, 0, 0, 7252, -225008]$$ $$10941048/12005$$ $$-46280744796160$$ $$$$ $$36864$$ $$1.3087$$

## Rank

sage: E.rank()

The elliptic curves in class 15680.bw have rank $$2$$.

## Complex multiplication

The elliptic curves in class 15680.bw do not have complex multiplication.

## Modular form 15680.2.a.bw

sage: E.q_eigenform(10)

$$q - q^{5} - 3q^{9} - 4q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 