# Properties

 Label 2736.d Number of curves $4$ Conductor $2736$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 2736.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.d1 2736v3 $$[0, 0, 0, -12607491, -17230231550]$$ $$74220219816682217473/16416$$ $$49017913344$$ $$$$ $$46080$$ $$2.3439$$
2736.d2 2736v2 $$[0, 0, 0, -787971, -269220350]$$ $$18120364883707393/269485056$$ $$804678065455104$$ $$[2, 2]$$ $$23040$$ $$1.9973$$
2736.d3 2736v4 $$[0, 0, 0, -764931, -285703166]$$ $$-16576888679672833/2216253521952$$ $$-6617697556492320768$$ $$$$ $$46080$$ $$2.3439$$
2736.d4 2736v1 $$[0, 0, 0, -50691, -3947006]$$ $$4824238966273/537919488$$ $$1606218984456192$$ $$$$ $$11520$$ $$1.6507$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2736.2.a.d

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 