# Properties

 Label 2646.a Number of curves $3$ Conductor $2646$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 2646.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2646.a1 2646g3 [1, -1, 0, -6036, 240848] [] 6804
2646.a2 2646g1 [1, -1, 0, -156, -722] [] 756 $$\Gamma_0(N)$$-optimal
2646.a3 2646g2 [1, -1, 0, 579, -3907] [] 2268

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2646.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 3q^{5} - q^{8} + 3q^{10} - 3q^{11} + 4q^{13} + q^{16} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 