Properties

Label 230640.cx
Number of curves $6$
Conductor $230640$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("230640.cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 230640.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
230640.cx1 230640cx6 [0, 1, 0, -4728427840, -125149388456140] [2] 94371840  
230640.cx2 230640cx4 [0, 1, 0, -295527040, -1955528903500] [2, 2] 47185920  
230640.cx3 230640cx5 [0, 1, 0, -290914240, -2019523200460] [2] 94371840  
230640.cx4 230640cx3 [0, 1, 0, -56891520, 128755058868] [4] 47185920  
230640.cx5 230640cx2 [0, 1, 0, -18759040, -29555745100] [2, 2] 23592960  
230640.cx6 230640cx1 [0, 1, 0, 922240, -1931100492] [2] 11796480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 230640.cx have rank \(1\).

Modular form 230640.2.a.cx

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.