Properties

Label 106a
Number of curves 2
Conductor 106
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("106.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 106a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106.c2 106a1 [1, 0, 0, 1, 1] [3] 6 \(\Gamma_0(N)\)-optimal
106.c1 106a2 [1, 0, 0, -9, -29] [] 18  

Rank

sage: E.rank()
 

The elliptic curves in class 106a have rank \(0\).

Modular form 106.2.a.c

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

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 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.