Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("22386.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22386s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.o3 22386s1 [1, 1, 1, -2104, -38023] [2] 15360 \(\Gamma_0(N)\)-optimal
22386.o2 22386s2 [1, 1, 1, -2184, -35079] [2, 2] 30720  
22386.o4 22386s3 [1, 1, 1, 3556, -182023] [2] 61440  
22386.o1 22386s4 [1, 1, 1, -9204, 301881] [4] 61440  

Rank

sage: E.rank()
 

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

Modular form 22386.2.a.o

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.