# Properties

 Label 2736.b Number of curves $2$ Conductor $2736$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 2736.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.b1 2736d2 $$[0, 0, 0, -2727, -54810]$$ $$445090032/19$$ $$95738112$$ $$$$ $$2688$$ $$0.61090$$
2736.b2 2736d1 $$[0, 0, 0, -162, -945]$$ $$-1492992/361$$ $$-113689008$$ $$$$ $$1344$$ $$0.26432$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2736.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2736.b do not have complex multiplication.

## Modular form2736.2.a.b

sage: E.q_eigenform(10)

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

## 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. 