# Properties

 Label 439569.o Number of curves $2$ Conductor $439569$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 439569.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.o1 439569o2 [1, -1, 1, -1793291, -923875234] [2] 4128768
439569.o2 439569o1 [1, -1, 1, -112586, -14277688] [2] 2064384 $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 439569.o1.

## Rank

sage: E.rank()

The elliptic curves in class 439569.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 439569.o do not have complex multiplication.

## Modular form 439569.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - 2q^{5} + 3q^{8} + 2q^{10} - q^{16} + 8q^{19} + O(q^{20})$$

## 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.