# Properties

 Label 9600.bk Number of curves $2$ Conductor $9600$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9600.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9600.bk1 9600r1 $$[0, 1, 0, -883, -10387]$$ $$19056256/27$$ $$108000000$$ $$[2]$$ $$3840$$ $$0.44462$$ $$\Gamma_0(N)$$-optimal
9600.bk2 9600r2 $$[0, 1, 0, -633, -16137]$$ $$-219488/729$$ $$-93312000000$$ $$[2]$$ $$7680$$ $$0.79119$$

## Rank

sage: E.rank()

The elliptic curves in class 9600.bk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9600.bk do not have complex multiplication.

## Modular form9600.2.a.bk

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.