# Properties

 Label 2646.bc Number of curves $2$ Conductor $2646$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 2646.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.bc1 2646q2 $$[1, -1, 1, -5081, 140753]$$ $$-10353819/8$$ $$-11206773144$$ $$$$ $$3780$$ $$0.86004$$
2646.bc2 2646q1 $$[1, -1, 1, 64, 809]$$ $$189/2$$ $$-311299254$$ $$[]$$ $$1260$$ $$0.31074$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2646.bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2646.bc do not have complex multiplication.

## Modular form2646.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 3q^{5} + q^{8} + 3q^{10} - 4q^{13} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 