# Properties

 Label 1560.k Number of curves $2$ Conductor $1560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 1560.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1560.k1 1560g2 $$[0, 1, 0, -200, 1008]$$ $$434163602/7605$$ $$15575040$$ $$$$ $$384$$ $$0.17662$$
1560.k2 1560g1 $$[0, 1, 0, 0, 48]$$ $$-4/975$$ $$-998400$$ $$$$ $$192$$ $$-0.16996$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1560.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1560.k do not have complex multiplication.

## Modular form1560.2.a.k

sage: E.q_eigenform(10)

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