Properties

Label 26.b
Number of curves $2$
Conductor $26$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26.b1 26b2 \([1, -1, 1, -213, -1257]\) \(-1064019559329/125497034\) \(-125497034\) \([]\) \(14\) \(0.28979\)  
26.b2 26b1 \([1, -1, 1, -3, 3]\) \(-2146689/1664\) \(-1664\) \([7]\) \(2\) \(-0.68316\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 26.2.a.b

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.