# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("4560.k1")

sage: E.isogeny_class()

## Elliptic curves in class 4560u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4560.k4 4560u1 [0, -1, 0, -160, -1280]  2304 $$\Gamma_0(N)$$-optimal
4560.k3 4560u2 [0, -1, 0, -3040, -63488] [2, 2] 4608
4560.k1 4560u3 [0, -1, 0, -48640, -4112768]  9216
4560.k2 4560u4 [0, -1, 0, -3520, -41600]  9216

## Rank

sage: E.rank()

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

## Modular form4560.2.a.k

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 