# Properties

 Label 8016.f Number of curves 2 Conductor 8016 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8016.f1")
sage: E.isogeny_class()

## Elliptic curves in class 8016.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
8016.f1 8016f2 [0, -1, 0, -1992, 34800] 2 6912
8016.f2 8016f1 [0, -1, 0, -72, 1008] 2 3456 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8016.f have rank $$0$$.

## Modular form8016.2.a.f

sage: E.q_eigenform(10)
$$q - q^{3} + 2q^{5} + 4q^{7} + q^{9} + 4q^{11} - 2q^{15} - 4q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 