Properties

Label 92.b
Number of curves 2
Conductor 92
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("92.b1")
sage: E.isogeny_class()

Elliptic curves in class 92.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
92.b1 92a2 [0, 1, 0, -18, -43] 1 6  
92.b2 92a1 [0, 1, 0, 2, 1] 3 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 92.b have rank \(0\).

Modular form 92.2.a.b

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

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 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.