# Properties

 Label 270802b Number of curves $2$ Conductor $270802$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 270802b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.b2 270802b1 $$[1, 0, 1, -3382, 69300]$$ $$7189057/644$$ $$383066218724$$ $$$$ $$537600$$ $$0.96239$$ $$\Gamma_0(N)$$-optimal
270802.b1 270802b2 $$[1, 0, 1, -11792, -415116]$$ $$304821217/51842$$ $$30836830607282$$ $$$$ $$1075200$$ $$1.3090$$

## Rank

sage: E.rank()

The elliptic curves in class 270802b have rank $$1$$.

## Complex multiplication

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

## Modular form 270802.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} - 2q^{5} + 2q^{6} + q^{7} - q^{8} + q^{9} + 2q^{10} - 6q^{11} - 2q^{12} - 4q^{13} - q^{14} + 4q^{15} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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. 