# Properties

 Label 560.d Number of curves $4$ Conductor $560$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 560.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
560.d1 560d4 $$[0, 0, 0, -4283, 107882]$$ $$2121328796049/120050$$ $$491724800$$ $$$$ $$384$$ $$0.73213$$
560.d2 560d3 $$[0, 0, 0, -1403, -18902]$$ $$74565301329/5468750$$ $$22400000000$$ $$$$ $$384$$ $$0.73213$$
560.d3 560d2 $$[0, 0, 0, -283, 1482]$$ $$611960049/122500$$ $$501760000$$ $$[2, 2]$$ $$192$$ $$0.38556$$
560.d4 560d1 $$[0, 0, 0, 37, 138]$$ $$1367631/2800$$ $$-11468800$$ $$$$ $$96$$ $$0.038988$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 560.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 560.d do not have complex multiplication.

## Modular form560.2.a.d

sage: E.q_eigenform(10)

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