Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("22386.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22386i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.m4 22386i1 [1, 0, 1, -575, 914] [2] 17280 \(\Gamma_0(N)\)-optimal
22386.m2 22386i2 [1, 0, 1, -5695, -164974] [2, 2] 34560  
22386.m3 22386i3 [1, 0, 1, -2335, -357166] [2] 69120  
22386.m1 22386i4 [1, 0, 1, -90975, -10569134] [2] 69120  

Rank

sage: E.rank()
 

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

Modular form 22386.2.a.m

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

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.