Properties

Label 86490.cd
Number of curves $4$
Conductor $86490$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 86490.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86490.cd1 86490bx4 \([1, -1, 1, -209198, 9679447]\) \(57960603/31250\) \(545897967285093750\) \([2]\) \(1451520\) \(2.0945\)  
86490.cd2 86490bx2 \([1, -1, 1, -122708, -16513569]\) \(8527173507/200\) \(4792519877400\) \([2]\) \(483840\) \(1.5452\)  
86490.cd3 86490bx1 \([1, -1, 1, -7388, -276513]\) \(-1860867/320\) \(-7668031803840\) \([2]\) \(241920\) \(1.1986\) \(\Gamma_0(N)\)-optimal
86490.cd4 86490bx3 \([1, -1, 1, 50272, 1168831]\) \(804357/500\) \(-8734367476561500\) \([2]\) \(725760\) \(1.7479\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86490.cd have rank \(1\).

Complex multiplication

The elliptic curves in class 86490.cd do not have complex multiplication.

Modular form 86490.2.a.cd

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 2 q^{7} + q^{8} - q^{10} + 6 q^{11} + 4 q^{13} + 2 q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.