# Properties

 Label 440818.bb Number of curves $2$ Conductor $440818$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 440818.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.bb1 440818bb2 $$[1, 1, 1, -828958, 271622107]$$ $$24553362849625/1755162752$$ $$4503267424899517568$$ $$[2]$$ $$11612160$$ $$2.3262$$ $$\Gamma_0(N)$$-optimal*
440818.bb2 440818bb1 $$[1, 1, 1, 47202, 18587099]$$ $$4533086375/60669952$$ $$-155662498079162368$$ $$[2]$$ $$5806080$$ $$1.9796$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 440818.bb1.

## Rank

sage: E.rank()

The elliptic curves in class 440818.bb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 440818.bb do not have complex multiplication.

## Modular form 440818.2.a.bb

sage: E.q_eigenform(10)

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

## 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 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.