# Properties

 Label 4560.f Number of curves $2$ Conductor $4560$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.f1 4560p2 $$[0, -1, 0, -116, -420]$$ $$680136784/38475$$ $$9849600$$ $$$$ $$768$$ $$0.096521$$
4560.f2 4560p1 $$[0, -1, 0, -21, 36]$$ $$67108864/16245$$ $$259920$$ $$$$ $$384$$ $$-0.25005$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.f

sage: E.q_eigenform(10)

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