Properties

Label 436425cd
Number of curves 2
Conductor 436425
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("436425.cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 436425cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
436425.cd2 436425cd1 [1, 0, 1, -304451, 940225673] [2] 12165120 \(\Gamma_0(N)\)-optimal*
436425.cd1 436425cd2 [1, 0, 1, -16372826, 25299882173] [2] 24330240 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 436425cd1.

Rank

sage: E.rank()
 

The elliptic curves in class 436425cd have rank \(1\).

Modular form 436425.2.a.cd

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + q^{6} - 2q^{7} - 3q^{8} + q^{9} - q^{11} - q^{12} - 2q^{13} - 2q^{14} - q^{16} + q^{18} - 2q^{19} + O(q^{20}) \)

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.