# Properties

 Label 4560.v Number of curves $2$ Conductor $4560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.v1 4560y2 $$[0, 1, 0, -1496, 21204]$$ $$90458382169/2671875$$ $$10944000000$$ $$$$ $$3072$$ $$0.70349$$
4560.v2 4560y1 $$[0, 1, 0, 24, 1140]$$ $$357911/135375$$ $$-554496000$$ $$$$ $$1536$$ $$0.35691$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.v

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 2 q^{7} + q^{9} + 2 q^{11} - 4 q^{13} - q^{15} + 2 q^{17} + q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 