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Properties

Label 83582.j
Number of curves $3$
Conductor $83582$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 83582.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83582.j1 83582d3 \([1, 0, 1, -2759540, 1764192370]\) \(15698803397448457/20709376\) \(3065730886795264\) \([]\) \(1425600\) \(2.2476\)  
83582.j2 83582d2 \([1, 0, 1, -43125, 1030080]\) \(59914169497/31554496\) \(4671197867306944\) \([]\) \(475200\) \(1.6983\)  
83582.j3 83582d1 \([1, 0, 1, -24610, -1487960]\) \(11134383337/316\) \(46779340924\) \([]\) \(158400\) \(1.1490\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 83582.j have rank \(2\).

Complex multiplication

The elliptic curves in class 83582.j do not have complex multiplication.

Modular form 83582.2.a.j

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.