# Properties

 Label 3528.b Number of curves $2$ Conductor $3528$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 3528.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3528.b1 3528ba2 $$[0, 0, 0, -17787, -902090]$$ $$3543122/49$$ $$8606801774592$$ $$[2]$$ $$9216$$ $$1.2876$$
3528.b2 3528ba1 $$[0, 0, 0, -147, -37730]$$ $$-4/7$$ $$-614771555328$$ $$[2]$$ $$4608$$ $$0.94102$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3528.2.a.b

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.