Properties

Label 129.b
Number of curves 4
Conductor \(129\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("129.b1")
sage: E.isogeny_class()

Elliptic curves in class 129.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
129.b1 129b3 [1, 0, 1, -245, 1433] 4 30  
129.b2 129b1 [1, 0, 1, -30, -29] 4 15 \(\Gamma_0(N)\)-optimal
129.b3 129b2 [1, 0, 1, -25, -49] 2 30  
129.b4 129b4 [1, 0, 1, 105, -191] 2 30  

Rank

sage: E.rank()

The elliptic curves in class 129.b have rank \(0\).

Modular form 129.2.1.b

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

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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