# Properties

 Label 528b Number of curves 4 Conductor 528 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("528.b1")

sage: E.isogeny_class()

## Elliptic curves in class 528b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.b4 528b1 [0, -1, 0, 1, -6]  48 $$\Gamma_0(N)$$-optimal
528.b3 528b2 [0, -1, 0, -44, -96] [2, 2] 96
528.b1 528b3 [0, -1, 0, -704, -6960]  192
528.b2 528b4 [0, -1, 0, -104, 288]  192

## Rank

sage: E.rank()

The elliptic curves in class 528b have rank $$0$$.

## Modular form528.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} - 4q^{7} + q^{9} + q^{11} + 6q^{13} + 2q^{15} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 