Properties

Label 26a
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 26a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26.a2 26a1 \([1, 0, 1, -5, -8]\) \(-10218313/17576\) \(-17576\) \([3]\) \(2\) \(-0.49492\) \(\Gamma_0(N)\)-optimal
26.a1 26a2 \([1, 0, 1, -460, -3830]\) \(-10730978619193/6656\) \(-6656\) \([]\) \(6\) \(0.054386\)  
26.a3 26a3 \([1, 0, 1, 0, 0]\) \(12167/26\) \(-26\) \([3]\) \(6\) \(-1.0442\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 26.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.