# Properties

 Label 3528y Number of curves $4$ Conductor $3528$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 3528y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.v4 3528y1 [0, 0, 0, -3234, 459277]  9216 $$\Gamma_0(N)$$-optimal
3528.v3 3528y2 [0, 0, 0, -111279, 14224210] [2, 2] 18432
3528.v2 3528y3 [0, 0, 0, -173019, -3322298]  36864
3528.v1 3528y4 [0, 0, 0, -1778259, 912726430]  36864

## Rank

sage: E.rank()

The elliptic curves in class 3528y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3528y do not have complex multiplication.

## Modular form3528.2.a.y

sage: E.q_eigenform(10)

$$q + 2q^{5} - 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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. 