Properties

Label 392784bv
Number of curves 2
Conductor 392784
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("392784.bv1")
sage: E.isogeny_class()

Elliptic curves in class 392784bv

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
392784.bv2 392784bv1 [0, 1, 0, -3544, -338668] 2 995328 \(\Gamma_0(N)\)-optimal*
392784.bv1 392784bv2 [0, 1, 0, -97624, -11741164] 2 1990656 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 270000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 392784bv1.

Rank

sage: E.rank()

The elliptic curves in class 392784bv have rank \(1\).

Modular form None

sage: E.q_eigenform(10)
\( q + q^{3} - 2q^{5} + q^{9} + 4q^{11} - 2q^{15} + 4q^{17} - 4q^{19} + O(q^{20}) \)

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 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.