Properties

Label 320790.ci
Number of curves $6$
Conductor $320790$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("320790.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 320790.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320790.ci1 320790ci3 [1, 0, 0, -98550451, 376553391905] [2] 35389440  
320790.ci2 320790ci6 [1, 0, 0, -87603131, -314228388759] [2] 70778880  
320790.ci3 320790ci4 [1, 0, 0, -8474931, 1065836961] [2, 2] 35389440  
320790.ci4 320790ci2 [1, 0, 0, -6162931, 5876184161] [2, 2] 17694720  
320790.ci5 320790ci1 [1, 0, 0, -244211, 159884385] [2] 8847360 \(\Gamma_0(N)\)-optimal
320790.ci6 320790ci5 [1, 0, 0, 33661269, 8507089881] [2] 70778880  

Rank

sage: E.rank()
 

The elliptic curves in class 320790.ci have rank \(1\).

Modular form 320790.2.a.ci

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.