# Properties

 Label 4560.s Number of curves $4$ Conductor $4560$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4560.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.s1 4560x3 $$[0, 1, 0, -9936, 377364]$$ $$26487576322129/44531250$$ $$182400000000$$ $$$$ $$6144$$ $$1.0561$$
4560.s2 4560x2 $$[0, 1, 0, -816, 1620]$$ $$14688124849/8122500$$ $$33269760000$$ $$[2, 2]$$ $$3072$$ $$0.70949$$
4560.s3 4560x1 $$[0, 1, 0, -496, -4396]$$ $$3301293169/22800$$ $$93388800$$ $$$$ $$1536$$ $$0.36292$$ $$\Gamma_0(N)$$-optimal
4560.s4 4560x4 $$[0, 1, 0, 3184, 16020]$$ $$871257511151/527800050$$ $$-2161869004800$$ $$$$ $$6144$$ $$1.0561$$

## Rank

sage: E.rank()

The elliptic curves in class 4560.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4560.s do not have complex multiplication.

## Modular form4560.2.a.s

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 4 q^{11} + 2 q^{13} - q^{15} + 2 q^{17} + q^{19} + O(q^{20})$$ ## 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. 