# Properties

 Label 1560.l Number of curves $4$ Conductor $1560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 1560.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1560.l1 1560h3 $$[0, 1, 0, -561600, -162177552]$$ $$19129597231400697604/26325$$ $$26956800$$ $$$$ $$6144$$ $$1.5921$$
1560.l2 1560h2 $$[0, 1, 0, -35100, -2542752]$$ $$18681746265374416/693005625$$ $$177409440000$$ $$[2, 2]$$ $$3072$$ $$1.2455$$
1560.l3 1560h4 $$[0, 1, 0, -33480, -2786400]$$ $$-4053153720264484/903687890625$$ $$-925376400000000$$ $$$$ $$6144$$ $$1.5921$$
1560.l4 1560h1 $$[0, 1, 0, -2295, -36450]$$ $$83587439220736/13990184325$$ $$223842949200$$ $$$$ $$1536$$ $$0.89895$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1560.2.a.l

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 