Properties

Label 439824dv
Number of curves $2$
Conductor $439824$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 439824dv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439824.dv2 439824dv1 [0, 1, 0, -9424, 282260] [2] 829440 \(\Gamma_0(N)\)-optimal*
439824.dv1 439824dv2 [0, 1, 0, -142704, 20700756] [2] 1658880 \(\Gamma_0(N)\)-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 439824dv1.

Rank

sage: E.rank()
 

The elliptic curves in class 439824dv have rank \(1\).

Complex multiplication

The elliptic curves in class 439824dv do not have complex multiplication.

Modular form 439824.2.a.dv

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{9} + q^{11} - 4q^{13} - 2q^{15} - q^{17} + 2q^{19} + O(q^{20}) \)

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.