Properties

Label 26.b
Number of curves 2
Conductor \(26\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("26.b1")
sage: E.isogeny_class()

Elliptic curves in class 26.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
26.b1 26b2 [1, -1, 1, -213, -1257] 1 14  
26.b2 26b1 [1, -1, 1, -3, 3] 7 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 26.b have rank \(0\).

Modular form 26.2.1.b

sage: E.q_eigenform(10)
\( q + q^{2} - 3q^{3} + q^{4} - q^{5} - 3q^{6} + q^{7} + q^{8} + 6q^{9} - q^{10} - 2q^{11} - 3q^{12} - q^{13} + q^{14} + 3q^{15} + q^{16} - 3q^{17} + 6q^{18} + 6q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)