Properties

Label 22386.ba
Number of curves 4
Conductor 22386
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22386.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22386.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.ba1 22386ba4 [1, 0, 0, -60253, -5035357] [2] 124416  
22386.ba2 22386ba2 [1, 0, 0, -14683, 682649] [6] 41472  
22386.ba3 22386ba1 [1, 0, 0, -643, 17153] [6] 20736 \(\Gamma_0(N)\)-optimal
22386.ba4 22386ba3 [1, 0, 0, 5657, -408475] [2] 62208  

Rank

sage: E.rank()
 

The elliptic curves in class 22386.ba have rank \(1\).

Modular form 22386.2.a.ba

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.