# Properties

 Label 5610.bk Number of curves $2$ Conductor $5610$ CM no Rank $1$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 5610.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bk1 5610bl2 $$[1, 0, 0, -9285, 236097]$$ $$88526309511756241/26991954000000$$ $$26991954000000$$ $$$$ $$21504$$ $$1.2821$$
5610.bk2 5610bl1 $$[1, 0, 0, 1595, 25025]$$ $$448733772344879/527357952000$$ $$-527357952000$$ $$$$ $$10752$$ $$0.93554$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5610.bk have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5610.bk do not have complex multiplication.

## Modular form5610.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 2 q^{13} - 4 q^{14} + q^{15} + q^{16} - q^{17} + q^{18} - 2 q^{19} + O(q^{20})$$

## 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. 