Properties

Label 39039.g
Number of curves $4$
Conductor $39039$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 39039.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.g1 39039j4 \([1, 1, 1, -1874467, -988571134]\) \(150902699857302457/59378319\) \(286607804554071\) \([2]\) \(580608\) \(2.1222\)  
39039.g2 39039j2 \([1, 1, 1, -117712, -15328864]\) \(37370253593737/730458729\) \(3525784767265761\) \([2, 2]\) \(290304\) \(1.7756\)  
39039.g3 39039j1 \([1, 1, 1, -15467, 375968]\) \(84778086457/35972937\) \(173634496068033\) \([4]\) \(145152\) \(1.4290\) \(\Gamma_0(N)\)-optimal
39039.g4 39039j3 \([1, 1, 1, 3123, -45150942]\) \(697864103/182466547263\) \(-880731172527973767\) \([2]\) \(580608\) \(2.1222\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39039.g have rank \(0\).

Complex multiplication

The elliptic curves in class 39039.g do not have complex multiplication.

Modular form 39039.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.