# Properties

 Label 3150.bk Number of curves $2$ Conductor $3150$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3150.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.bk1 3150bq1 $$[1, -1, 1, -725, -723]$$ $$461889917/263424$$ $$24004512000$$ $$$$ $$3072$$ $$0.68159$$ $$\Gamma_0(N)$$-optimal
3150.bk2 3150bq2 $$[1, -1, 1, 2875, -7923]$$ $$28849701763/16941456$$ $$-1543790178000$$ $$$$ $$6144$$ $$1.0282$$

## Rank

sage: E.rank()

The elliptic curves in class 3150.bk have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3150.bk do not have complex multiplication.

## Modular form3150.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 2q^{11} - 6q^{13} + q^{14} + q^{16} + 4q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 