# Properties

 Label 270802.o Number of curves $2$ Conductor $270802$ CM no Rank $0$ Graph

# Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 270802.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.o1 270802o2 $$[1, -1, 1, -200316, 34450001]$$ $$1494447319737/5411854$$ $$3219096969047134$$ $$[2]$$ $$2408448$$ $$1.8367$$
270802.o2 270802o1 $$[1, -1, 1, -6886, 1025297]$$ $$-60698457/725788$$ $$-431715628501948$$ $$[2]$$ $$1204224$$ $$1.4901$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 270802.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 270802.o do not have complex multiplication.

## Modular form 270802.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 2q^{5} + q^{7} + q^{8} - 3q^{9} - 2q^{10} + 4q^{11} + 4q^{13} + q^{14} + q^{16} + 8q^{17} - 3q^{18} + 2q^{19} + O(q^{20})$$

## 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.