# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.x1 4560bc3 $$[0, 1, 0, -7879680, -8516182860]$$ $$13209596798923694545921/92340$$ $$378224640$$ $$$$ $$92160$$ $$2.1806$$
4560.x2 4560bc4 $$[0, 1, 0, -498560, -129737292]$$ $$3345930611358906241/165622259047500$$ $$678388773058560000$$ $$$$ $$92160$$ $$2.1806$$
4560.x3 4560bc2 $$[0, 1, 0, -492480, -133188300]$$ $$3225005357698077121/8526675600$$ $$34925263257600$$ $$[2, 2]$$ $$46080$$ $$1.8341$$
4560.x4 4560bc1 $$[0, 1, 0, -30400, -2142412]$$ $$-758575480593601/40535043840$$ $$-166031539568640$$ $$$$ $$23040$$ $$1.4875$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.x

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4 q^{7} + q^{9} - 6 q^{13} + q^{15} + 2 q^{17} - q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 