# Properties

 Label 474320br Number of curves $2$ Conductor $474320$ CM no Rank $2$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 474320br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
474320.br2 474320br1 $$[0, 1, 0, 4800, 141700]$$ $$19652/25$$ $$-15555722828800$$ $$[2]$$ $$983040$$ $$1.2173$$ $$\Gamma_0(N)$$-optimal*
474320.br1 474320br2 $$[0, 1, 0, -29080, 1347828]$$ $$2185454/625$$ $$777786141440000$$ $$[2]$$ $$1966080$$ $$1.5638$$ $$\Gamma_0(N)$$-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 474320br1.

## Rank

sage: E.rank()

The elliptic curves in class 474320br have rank $$2$$.

## Complex multiplication

The elliptic curves in class 474320br do not have complex multiplication.

## Modular form 474320.2.a.br

sage: E.q_eigenform(10)

$$q - 2 q^{3} + q^{5} + q^{9} - 2 q^{13} - 2 q^{15} + 2 q^{19} + O(q^{20})$$

## 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.