# Properties

 Label 1008d Number of curves 2 Conductor 1008 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1008.f1")
sage: E.isogeny_class()

## Elliptic curves in class 1008d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1008.f2 1008d1 [0, 0, 0, -6, -9] 2 64 $$\Gamma_0(N)$$-optimal
1008.f1 1008d2 [0, 0, 0, -111, -450] 2 128

## Rank

sage: E.rank()

The elliptic curves in class 1008d have rank $$0$$.

## Modular form1008.2.a.f

sage: E.q_eigenform(10)
$$q - 2q^{5} + q^{7} + 2q^{11} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 