# Properties

 Label 4560.u Number of curves $2$ Conductor $4560$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.u1 4560v2 $$[0, 1, 0, -3476, -72360]$$ $$18148802937424/1947796875$$ $$498636000000$$ $$[2]$$ $$4608$$ $$0.97878$$
4560.u2 4560v1 $$[0, 1, 0, -3381, -76806]$$ $$267219216891904/3655125$$ $$58482000$$ $$[2]$$ $$2304$$ $$0.63221$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4560.u have rank $$1$$.

## Complex multiplication

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

## Modular form4560.2.a.u

sage: E.q_eigenform(10)

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

## 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.