# Properties

 Label 128.a Number of curves 2 Conductor 128 CM no Rank 1 Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("128.a1")
sage: E.isogeny_class()

## Elliptic curves in class 128.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
128.a1 128a2 [0, 1, 0, -9, 7] 2 8
128.a2 128a1 [0, 1, 0, 1, 1] 2 4 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 128.a have rank $$1$$.

## Modular form128.2.a.a

sage: E.q_eigenform(10)
$$q - 2q^{3} - 2q^{5} - 4q^{7} + q^{9} + 2q^{11} - 2q^{13} + 4q^{15} - 2q^{17} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 