# Properties

 Label 528g Number of curves 4 Conductor 528 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("528.d1")

sage: E.isogeny_class()

## Elliptic curves in class 528g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.d3 528g1 [0, -1, 0, -88, -272]  96 $$\Gamma_0(N)$$-optimal
528.d4 528g2 [0, -1, 0, 72, -1296]  192
528.d1 528g3 [0, -1, 0, -1288, 18160]  288
528.d2 528g4 [0, -1, 0, -648, 35568]  576

## Rank

sage: E.rank()

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

## Modular form528.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} + q^{11} - 4q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 