# Properties

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

Show commands: SageMath
E = EllipticCurve("s1")

E.isogeny_class()

## Elliptic curves in class 2736.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.s1 2736t3 $$[0, 0, 0, -14619, 680330]$$ $$115714886617/1539$$ $$4595429376$$ $$$$ $$3072$$ $$0.99745$$
2736.s2 2736t2 $$[0, 0, 0, -939, 10010]$$ $$30664297/3249$$ $$9701462016$$ $$[2, 2]$$ $$1536$$ $$0.65087$$
2736.s3 2736t1 $$[0, 0, 0, -219, -1078]$$ $$389017/57$$ $$170201088$$ $$$$ $$768$$ $$0.30430$$ $$\Gamma_0(N)$$-optimal
2736.s4 2736t4 $$[0, 0, 0, 1221, 49322]$$ $$67419143/390963$$ $$-1167409262592$$ $$$$ $$3072$$ $$0.99745$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2736.2.a.s

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 