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Properties

Label 132878.j
Number of curves $3$
Conductor $132878$
CM no
Rank $0$
Graph

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

Elliptic curves in class 132878.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132878.j1 132878b3 \([1, 1, 1, -4387094, -3538648557]\) \(15698803397448457/20709376\) \(12318419808157696\) \([]\) \(3024000\) \(2.3635\)  
132878.j2 132878b2 \([1, 1, 1, -68559, -2100587]\) \(59914169497/31554496\) \(18769350103201216\) \([]\) \(1008000\) \(1.8142\)  
132878.j3 132878b1 \([1, 1, 1, -39124, 2962233]\) \(11134383337/316\) \(187964169436\) \([]\) \(336000\) \(1.2649\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 132878.j have rank \(0\).

Complex multiplication

The elliptic curves in class 132878.j do not have complex multiplication.

Modular form 132878.2.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.