Properties

Label 178a
Number of curves 2
Conductor 178
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("178.b1")
sage: E.isogeny_class()

Elliptic curves in class 178a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
178.b2 178a1 [1, 0, 0, 6, -28] 3 32 \(\Gamma_0(N)\)-optimal
178.b1 178a2 [1, 0, 0, -554, -5068] 1 96  

Rank

sage: E.rank()

The elliptic curves in class 178a have rank \(0\).

Modular form 178.2.a.b

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

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 Cremona 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 Cremona labels.