# Properties

 Label 15600.bk Number of curves $4$ Conductor $15600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bk1")

sage: E.isogeny_class()

## Elliptic curves in class 15600.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bk1 15600bd3 $$[0, -1, 0, -8295808, -9194021888]$$ $$986551739719628473/111045168$$ $$7106890752000000$$ $$$$ $$491520$$ $$2.4659$$
15600.bk2 15600bd4 $$[0, -1, 0, -935808, 118490112]$$ $$1416134368422073/725251155408$$ $$46416073946112000000$$ $$$$ $$491520$$ $$2.4659$$
15600.bk3 15600bd2 $$[0, -1, 0, -519808, -142757888]$$ $$242702053576633/2554695936$$ $$163500539904000000$$ $$[2, 2]$$ $$245760$$ $$2.1194$$
15600.bk4 15600bd1 $$[0, -1, 0, -7808, -5541888]$$ $$-822656953/207028224$$ $$-13249806336000000$$ $$$$ $$122880$$ $$1.7728$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15600.bk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 15600.bk do not have complex multiplication.

## Modular form 15600.2.a.bk

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{7} + q^{9} + 4q^{11} - q^{13} - 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 