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Properties

Label 26.a
Number of curves $3$
Conductor $26$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26.a1 26a2 [1, 0, 1, -460, -3830] [] 6  
26.a2 26a1 [1, 0, 1, -5, -8] [3] 2 \(\Gamma_0(N)\)-optimal
26.a3 26a3 [1, 0, 1, 0, 0] [3] 6  

Rank

sage: E.rank()
 

The elliptic curves in class 26.a have rank \(0\).

Complex multiplication

The elliptic curves in class 26.a do not have complex multiplication.

Modular form 26.2.a.a

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

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.