# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("528.j1")

sage: E.isogeny_class()

## Elliptic curves in class 528j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.j4 528j1 [0, 1, 0, -32, -12]  96 $$\Gamma_0(N)$$-optimal
528.j2 528j2 [0, 1, 0, -352, 2420] [2, 2] 192
528.j1 528j3 [0, 1, 0, -5632, 160820]  384
528.j3 528j4 [0, 1, 0, -192, 4788]  384

## Rank

sage: E.rank()

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

## Modular form528.2.a.j

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 