Properties

Label 83790ck
Number of curves $4$
Conductor $83790$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("83790.cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 83790ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
83790.cl4 83790ck1 [1, -1, 0, -4419, 194053] [2] 221184 \(\Gamma_0(N)\)-optimal
83790.cl3 83790ck2 [1, -1, 0, -83799, 9354505] [2, 2] 442368  
83790.cl2 83790ck3 [1, -1, 0, -97029, 6213703] [2] 884736  
83790.cl1 83790ck4 [1, -1, 0, -1340649, 597811675] [2] 884736  

Rank

sage: E.rank()
 

The elliptic curves in class 83790ck have rank \(1\).

Modular form 83790.2.a.cl

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 4q^{11} + 2q^{13} + q^{16} - 2q^{17} + q^{19} + O(q^{20}) \)

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 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.