Properties

Label 89232y
Number of curves 4
Conductor 89232
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("89232.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 89232y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
89232.q3 89232y1 [0, -1, 0, -14928, -657216] [2] 207360 \(\Gamma_0(N)\)-optimal
89232.q4 89232y2 [0, -1, 0, 12112, -2798784] [2] 414720  
89232.q1 89232y3 [0, -1, 0, -217728, 39026688] [2] 622080  
89232.q2 89232y4 [0, -1, 0, -109568, 77704704] [2] 1244160  

Rank

sage: E.rank()
 

The elliptic curves in class 89232y have rank \(0\).

Modular form 89232.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{7} + q^{9} - q^{11} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.