# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("4560.s1")

sage: E.isogeny_class()

## Elliptic curves in class 4560x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4560.s3 4560x1 [0, 1, 0, -496, -4396]  1536 $$\Gamma_0(N)$$-optimal
4560.s2 4560x2 [0, 1, 0, -816, 1620] [2, 2] 3072
4560.s1 4560x3 [0, 1, 0, -9936, 377364]  6144
4560.s4 4560x4 [0, 1, 0, 3184, 16020]  6144

## Rank

sage: E.rank()

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

## Modular form4560.2.a.s

sage: E.q_eigenform(10)

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

## 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. 