# Properties

 Label 4560.n Number of curves $6$ Conductor $4560$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.n1 4560d5 $$[0, -1, 0, -693120, 222337440]$$ $$17981241677724245762/16245$$ $$33269760$$ $$[4]$$ $$16384$$ $$1.6386$$
4560.n2 4560d4 $$[0, -1, 0, -43320, 3484800]$$ $$8780093172522724/263900025$$ $$270233625600$$ $$[2, 4]$$ $$8192$$ $$1.2920$$
4560.n3 4560d6 $$[0, -1, 0, -41520, 3785760]$$ $$-3865238121540962/764260336845$$ $$-1565205169858560$$ $$[4]$$ $$16384$$ $$1.6386$$
4560.n4 4560d3 $$[0, -1, 0, -12320, -474000]$$ $$201971983086724/20447192475$$ $$20937925094400$$ $$[2]$$ $$8192$$ $$1.2920$$
4560.n5 4560d2 $$[0, -1, 0, -2820, 50400]$$ $$9691367618896/1480325625$$ $$378963360000$$ $$[2, 2]$$ $$4096$$ $$0.94545$$
4560.n6 4560d1 $$[0, -1, 0, 305, 4150]$$ $$195469297664/601171875$$ $$-9618750000$$ $$[2]$$ $$2048$$ $$0.59887$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.n

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.