Properties

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

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

Elliptic curves in class 474320.br

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

Rank

sage: E.rank()
 

The elliptic curves in class 474320.br have rank \(2\).

Complex multiplication

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

Modular form 474320.2.a.br

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} + q^{9} - 2 q^{13} - 2 q^{15} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.