# Properties

 Label 528.a Number of curves 4 Conductor 528 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("528.a1")

sage: E.isogeny_class()

## Elliptic curves in class 528.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.a1 528f3 [0, -1, 0, -161040, 24927936] [2] 2400
528.a2 528f4 [0, -1, 0, -160880, 24979776] [2] 4800
528.a3 528f1 [0, -1, 0, -720, -5184] [2] 480 $$\Gamma_0(N)$$-optimal
528.a4 528f2 [0, -1, 0, 1840, -35904] [2] 960

## Rank

sage: E.rank()

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

## Modular form528.2.a.a

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.