# Properties

 Label 9702.bk Number of curves $2$ Conductor $9702$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 9702.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bk1 9702bu2 $$[1, -1, 1, -650390, -201724491]$$ $$121681065322255375/12702096$$ $$3176120998512$$ $$[2]$$ $$65536$$ $$1.8278$$
9702.bk2 9702bu1 $$[1, -1, 1, -40550, -3160587]$$ $$-29489309167375/303595776$$ $$-75913213001472$$ $$[2]$$ $$32768$$ $$1.4812$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9702.bk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9702.bk do not have complex multiplication.

## Modular form9702.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - q^{11} - 4 q^{13} + q^{16} - 4 q^{17} + O(q^{20})$$

## 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.