# Properties

 Label 4560.d Number of curves $2$ Conductor $4560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.d1 4560m2 $$[0, -1, 0, -373216, 87882880]$$ $$1403607530712116449/39475350$$ $$161691033600$$ $$$$ $$26880$$ $$1.6612$$
4560.d2 4560m1 $$[0, -1, 0, -23296, 1382656]$$ $$-341370886042369/1817528220$$ $$-7444595589120$$ $$$$ $$13440$$ $$1.3146$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 2 q^{7} + q^{9} + 4 q^{11} + 6 q^{13} + q^{15} + 4 q^{17} - q^{19} + O(q^{20})$$ ## 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. 