# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 270802r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.r2 270802r1 $$[1, -1, 1, -43379779, 109983131651]$$ $$-15177411906818559273/167619938752$$ $$-99704248634281235392$$ $$$$ $$23224320$$ $$2.9912$$ $$\Gamma_0(N)$$-optimal
270802.r1 270802r2 $$[1, -1, 1, -694078299, 7038360693203]$$ $$62167173500157644301993/7582456$$ $$4510221659256376$$ $$$$ $$46448640$$ $$3.3378$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 270802.2.a.r

sage: E.q_eigenform(10)

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