# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.q1 4560t4 $$[0, -1, 0, -15480, 746352]$$ $$100162392144121/23457780$$ $$96083066880$$ $$$$ $$12288$$ $$1.0978$$
4560.q2 4560t3 $$[0, -1, 0, -7160, -224400]$$ $$9912050027641/311647500$$ $$1276508160000$$ $$$$ $$12288$$ $$1.0978$$
4560.q3 4560t2 $$[0, -1, 0, -1080, 9072]$$ $$34043726521/11696400$$ $$47908454400$$ $$[2, 2]$$ $$6144$$ $$0.75126$$
4560.q4 4560t1 $$[0, -1, 0, 200, 880]$$ $$214921799/218880$$ $$-896532480$$ $$$$ $$3072$$ $$0.40469$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 4q^{7} + q^{9} + 4q^{11} - 6q^{13} - q^{15} - 6q^{17} + q^{19} + O(q^{20})$$ ## 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. 