# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 270802s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.s2 270802s1 $$[1, -1, 1, -33279369, -74033947255]$$ $$-6852688047169144713/15901562765312$$ $$-9458620373152827441152$$ $$$$ $$23224320$$ $$3.0976$$ $$\Gamma_0(N)$$-optimal
270802.s1 270802s2 $$[1, -1, 1, -532766089, -4733046276727]$$ $$28115476317271727409033/150871003136$$ $$89741591127956934656$$ $$$$ $$46448640$$ $$3.4442$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 270802.2.a.s

sage: E.q_eigenform(10)

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