Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("89232.cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 89232co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
89232.cs3 89232co1 [0, 1, 0, -17632, 887732] [2] 221184 \(\Gamma_0(N)\)-optimal
89232.cs2 89232co2 [0, 1, 0, -31152, -675180] [2, 2] 442368  
89232.cs4 89232co3 [0, 1, 0, 117568, -5136780] [2] 884736  
89232.cs1 89232co4 [0, 1, 0, -396192, -96023628] [2] 884736  

Rank

sage: E.rank()
 

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

Modular form 89232.2.a.cs

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + 4q^{7} + q^{9} + q^{11} + 2q^{15} - 2q^{17} + O(q^{20}) \)

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.