# Properties

 Label 70560.dy Number of curves $4$ Conductor $70560$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dy1")

sage: E.isogeny_class()

## Elliptic curves in class 70560.dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70560.dy1 70560bt4 $$[0, 0, 0, -494067, -133667786]$$ $$303735479048/105$$ $$4610786664960$$ $$[2]$$ $$589824$$ $$1.7858$$
70560.dy2 70560bt3 $$[0, 0, 0, -64092, 3117184]$$ $$82881856/36015$$ $$12651998608650240$$ $$[2]$$ $$589824$$ $$1.7858$$
70560.dy3 70560bt1 $$[0, 0, 0, -31017, -2068976]$$ $$601211584/11025$$ $$60516574977600$$ $$[2, 2]$$ $$294912$$ $$1.4393$$ $$\Gamma_0(N)$$-optimal
70560.dy4 70560bt2 $$[0, 0, 0, -147, -6001814]$$ $$-8/354375$$ $$-15561404994240000$$ $$[2]$$ $$589824$$ $$1.7858$$

## Rank

sage: E.rank()

The elliptic curves in class 70560.dy have rank $$0$$.

## Complex multiplication

The elliptic curves in class 70560.dy do not have complex multiplication.

## Modular form 70560.2.a.dy

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.