Properties

Label 108a
Number of curves 2
Conductor 108
CM -3
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("108.a1")
sage: E.isogeny_class()

Elliptic curves in class 108a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
108.a2 108a1 [0, 0, 0, 0, 4] 3 6 \(\Gamma_0(N)\)-optimal
108.a1 108a2 [0, 0, 0, 0, -108] 1 18  

Rank

sage: E.rank()

The elliptic curves in class 108a have rank \(0\).

Modular form 108.2.a.a

sage: E.q_eigenform(10)
\( q + 5q^{7} - 7q^{13} - q^{19} + O(q^{20}) \)

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.