# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 270802e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.e2 270802e1 $$[1, -1, 0, -332130821, -2329675891243]$$ $$6811821555839776164753/16312107262976$$ $$9702821814671604663296$$ $$$$ $$45158400$$ $$3.4600$$ $$\Gamma_0(N)$$-optimal
270802.e1 270802e2 $$[1, -1, 0, -336033061, -2272124875275]$$ $$7054751972146948898193/332947845138448288$$ $$198045142965045515454924448$$ $$$$ $$90316800$$ $$3.8066$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 270802.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2q^{5} - q^{7} - q^{8} - 3q^{9} - 2q^{10} - 4q^{11} + q^{14} + q^{16} + 6q^{17} + 3q^{18} - 4q^{19} + O(q^{20})$$ ## 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 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. 