# Properties

 Label 560d Number of curves $4$ Conductor $560$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("560.d1")

sage: E.isogeny_class()

## Elliptic curves in class 560d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
560.d4 560d1 [0, 0, 0, 37, 138] [2] 96 $$\Gamma_0(N)$$-optimal
560.d3 560d2 [0, 0, 0, -283, 1482] [2, 2] 192
560.d2 560d3 [0, 0, 0, -1403, -18902] [2] 384
560.d1 560d4 [0, 0, 0, -4283, 107882] [4] 384

## Rank

sage: E.rank()

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

## 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 Cremona 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 Cremona labels.