# Properties

 Label 3528q Number of curves $2$ Conductor $3528$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 3528q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.e2 3528q1 [0, 0, 0, -2646, 83349]  4608 $$\Gamma_0(N)$$-optimal
3528.e1 3528q2 [0, 0, 0, -48951, 4167450]  9216

## Rank

sage: E.rank()

The elliptic curves in class 3528q have rank $$1$$.

## Complex multiplication

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

## Modular form3528.2.a.q

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 