# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 270802.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.i1 270802i2 $$[1, 1, 0, -33437336, 74402815040]$$ $$6950735348004218737/462042447104$$ $$274833622829368112384$$ $$$$ $$30965760$$ $$2.9777$$
270802.i2 270802i1 $$[1, 1, 0, -2219416, 1009485120]$$ $$2032601155983217/434808356864$$ $$258634150828397625344$$ $$$$ $$15482880$$ $$2.6311$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 270802.2.a.i

sage: E.q_eigenform(10)

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