# Properties

 Label 528.c Number of curves 2 Conductor 528 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("528.c1")

sage: E.isogeny_class()

## Elliptic curves in class 528.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.c1 528a1 [0, -1, 0, -8, 0]  32 $$\Gamma_0(N)$$-optimal
528.c2 528a2 [0, -1, 0, 32, -32]  64

## Rank

sage: E.rank()

The elliptic curves in class 528.c have rank $$1$$.

## Modular form528.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} - q^{11} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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. 