# Properties

 Label 2736.o Number of curves $4$ Conductor $2736$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 2736.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.o1 2736n3 $$[0, 0, 0, -61635, -5889598]$$ $$8671983378625/82308$$ $$245770371072$$ $$$$ $$6912$$ $$1.3480$$
2736.o2 2736n4 $$[0, 0, 0, -60195, -6177886]$$ $$-8078253774625/846825858$$ $$-2528608462774272$$ $$$$ $$13824$$ $$1.6945$$
2736.o3 2736n1 $$[0, 0, 0, -1155, 1154]$$ $$57066625/32832$$ $$98035826688$$ $$$$ $$2304$$ $$0.79865$$ $$\Gamma_0(N)$$-optimal
2736.o4 2736n2 $$[0, 0, 0, 4605, 9218]$$ $$3616805375/2105352$$ $$-6286547386368$$ $$$$ $$4608$$ $$1.1452$$

## Rank

sage: E.rank()

The elliptic curves in class 2736.o have rank $$1$$.

## Complex multiplication

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

## Modular form2736.2.a.o

sage: E.q_eigenform(10)

$$q + 4q^{7} - 4q^{13} - 6q^{17} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 