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Properties

Label 4026.e
Number of curves $2$
Conductor $4026$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4026.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4026.e1 4026b2 \([1, 0, 1, -202144, 32870414]\) \(913488720932053621369/61400271112522848\) \(61400271112522848\) \([2]\) \(116640\) \(1.9703\)  
4026.e2 4026b1 \([1, 0, 1, 10816, 2204174]\) \(139952759660884871/2178096890821632\) \(-2178096890821632\) \([2]\) \(58320\) \(1.6237\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4026.e have rank \(0\).

Complex multiplication

The elliptic curves in class 4026.e do not have complex multiplication.

Modular form 4026.2.a.e

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.