Properties

Label 116.b
Number of curves 2
Conductor 116
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("116.b1")
sage: E.isogeny_class()

Elliptic curves in class 116.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
116.b1 116b1 [0, 1, 0, -4, 4] 3 8 \(\Gamma_0(N)\)-optimal
116.b2 116b2 [0, 1, 0, 36, -76] 1 24  

Rank

sage: E.rank()

The elliptic curves in class 116.b have rank \(0\).

Modular form 116.2.a.b

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

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.