# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("528.g1")

sage: E.isogeny_class()

## Elliptic curves in class 528.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.g1 528h3 [0, 1, 0, -2344, -44428]  384
528.g2 528h2 [0, 1, 0, -184, -364] [2, 2] 192
528.g3 528h1 [0, 1, 0, -104, 372]  96 $$\Gamma_0(N)$$-optimal
528.g4 528h4 [0, 1, 0, 696, -2124]  384

## Rank

sage: E.rank()

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

## Modular form528.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 