Properties

Label 4026.e
Number of curves 2
Conductor 4026
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4026.e1")
sage: E.isogeny_class()

Elliptic curves in class 4026.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4026.e1 4026b2 [1, 0, 1, -202144, 32870414] 2 116640  
4026.e2 4026b1 [1, 0, 1, 10816, 2204174] 2 58320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 4026.e have rank \(0\).

Modular form 4026.2.a.e

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} + q^{4} + 4q^{5} - q^{6} + 4q^{7} - q^{8} + q^{9} - 4q^{10} - q^{11} + q^{12} + 6q^{13} - 4q^{14} + 4q^{15} + q^{16} - 6q^{17} - q^{18} + O(q^{20}) \)

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 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.