# Properties

 Label 270802.a Number of curves $2$ Conductor $270802$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 270802.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.a1 270802a2 $$[1, 0, 1, -14317202, 9417363594]$$ $$545644947830040577/251340262104722$$ $$149503049406141189821762$$ $$$$ $$30105600$$ $$3.1415$$
270802.a2 270802a1 $$[1, 0, 1, -7244392, -7404607710]$$ $$70687311717054817/1093629002564$$ $$650516035247035995044$$ $$$$ $$15052800$$ $$2.7950$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 270802.a have rank $$2$$.

## Complex multiplication

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

## Modular form 270802.2.a.a

sage: E.q_eigenform(10)

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