# Properties

 Label 270802j Number of curves $2$ Conductor $270802$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 270802j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.j2 270802j1 $$[1, 1, 0, 77355, -154723]$$ $$86058173375/49827568$$ $$-29638599475113328$$ $$$$ $$2257920$$ $$1.8501$$ $$\Gamma_0(N)$$-optimal
270802.j1 270802j2 $$[1, 1, 0, -309505, -1624791]$$ $$5512402554625/3188422748$$ $$1896548207717306108$$ $$$$ $$4515840$$ $$2.1967$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 270802.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - q^{7} - q^{8} + q^{9} - 4q^{11} + 2q^{12} - 2q^{13} + q^{14} + q^{16} - 4q^{17} - q^{18} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 