Properties

Label 22386.u
Number of curves 2
Conductor 22386
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22386.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22386.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.u1 22386bc2 [1, 0, 0, -10303962, -12729674844] [] 1306368  
22386.u2 22386bc1 [1, 0, 0, -307482, 41491044] [3] 435456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 22386.2.a.u

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.