# Properties

 Label 333270.bo Number of curves $2$ Conductor $333270$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bo1")

sage: E.isogeny_class()

## Elliptic curves in class 333270.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.bo1 333270bo2 $$[1, -1, 0, -119596419, -365993076267]$$ $$1753007192038126081/478174101507200$$ $$51603670667564657495683200$$ $$$$ $$113541120$$ $$3.6416$$
333270.bo2 333270bo1 $$[1, -1, 0, -43420419, 105551598933]$$ $$83890194895342081/3958384640000$$ $$427181599116845475840000$$ $$$$ $$56770560$$ $$3.2950$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 333270.bo have rank $$0$$.

## Complex multiplication

The elliptic curves in class 333270.bo do not have complex multiplication.

## Modular form 333270.2.a.bo

sage: E.q_eigenform(10)

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