# Properties

 Label 2646.w Number of curves $2$ Conductor $2646$ CM no Rank $1$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 2646.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.w1 2646s1 $$[1, -1, 1, -20, 39]$$ $$-637875/16$$ $$-21168$$ $$[]$$ $$288$$ $$-0.38564$$ $$\Gamma_0(N)$$-optimal
2646.w2 2646s2 $$[1, -1, 1, 85, 123]$$ $$5767125/4096$$ $$-48771072$$ $$[]$$ $$864$$ $$0.16367$$

## Rank

sage: E.rank()

The elliptic curves in class 2646.w have rank $$1$$.

## Complex multiplication

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

## Modular form2646.2.a.w

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 6q^{11} - 5q^{13} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 