# Properties

 Label 1560.a Number of curves $4$ Conductor $1560$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 1560.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1560.a1 1560i4 $$[0, -1, 0, -7696, 261820]$$ $$49235161015876/137109375$$ $$140400000000$$ $$[2]$$ $$1536$$ $$1.0115$$
1560.a2 1560i3 $$[0, -1, 0, -7176, -230724]$$ $$39914580075556/172718325$$ $$176863564800$$ $$[2]$$ $$1536$$ $$1.0115$$
1560.a3 1560i2 $$[0, -1, 0, -676, 676]$$ $$133649126224/77000625$$ $$19712160000$$ $$[2, 2]$$ $$768$$ $$0.66494$$
1560.a4 1560i1 $$[0, -1, 0, 169, 0]$$ $$33165879296/19278675$$ $$-308458800$$ $$[4]$$ $$384$$ $$0.31837$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1560.a have rank $$1$$.

## Complex multiplication

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

## Modular form1560.2.a.a

sage: E.q_eigenform(10)

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

## 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.