# Properties

 Label 32340.bk Number of curves $2$ Conductor $32340$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 32340.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bk1 32340bl2 $$[0, 1, 0, -19420, 1034900]$$ $$26894628304/9075$$ $$273322156800$$ $$[2]$$ $$69120$$ $$1.1666$$
32340.bk2 32340bl1 $$[0, 1, 0, -1045, 20600]$$ $$-67108864/61875$$ $$-116472510000$$ $$[2]$$ $$34560$$ $$0.82005$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32340.bk have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32340.bk do not have complex multiplication.

## Modular form 32340.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - q^{11} - 2q^{13} + q^{15} - 8q^{17} + 2q^{19} + O(q^{20})$$

## 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.