Properties

Label 43890.ct
Number of curves 8
Conductor 43890
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("43890.ct1")
sage: E.isogeny_class()

Elliptic curves in class 43890.ct

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
43890.ct1 43890ct7 [1, 0, 0, -150608156, -711423835980] 2 5971968  
43890.ct2 43890ct8 [1, 0, 0, -18882436, 14644625516] 2 5971968  
43890.ct3 43890ct5 [1, 0, 0, -15906496, 24416653760] 6 1990656  
43890.ct4 43890ct6 [1, 0, 0, -9449936, -11024979984] 4 2985984  
43890.ct5 43890ct4 [1, 0, 0, -2148416, -652538304] 6 1990656  
43890.ct6 43890ct2 [1, 0, 0, -999296, 377303040] 12 995328  
43890.ct7 43890ct3 [1, 0, 0, -38016, -481747200] 2 1492992  
43890.ct8 43890ct1 [1, 0, 0, 4224, 17842176] 6 497664 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 43890.ct have rank \(0\).

Modular form None

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 2q^{13} + q^{14} - q^{15} + q^{16} + 6q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 12 & 2 & 3 & 6 & 4 & 12 \\ 4 & 1 & 3 & 2 & 12 & 6 & 4 & 12 \\ 12 & 3 & 1 & 6 & 4 & 2 & 12 & 4 \\ 2 & 2 & 6 & 1 & 6 & 3 & 2 & 6 \\ 3 & 12 & 4 & 6 & 1 & 2 & 12 & 4 \\ 6 & 6 & 2 & 3 & 2 & 1 & 6 & 2 \\ 4 & 4 & 12 & 2 & 12 & 6 & 1 & 3 \\ 12 & 12 & 4 & 6 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.