Properties

Label 95139a
Number of curves $2$
Conductor $95139$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 95139a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95139.j2 95139a1 \([1, -1, 0, -14595, -122032]\) \(19683/11\) \(192156084484353\) \([2]\) \(362880\) \(1.4310\) \(\Gamma_0(N)\)-optimal
95139.j1 95139a2 \([1, -1, 0, -144330, 21024773]\) \(19034163/121\) \(2113716929327883\) \([2]\) \(725760\) \(1.7776\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95139a have rank \(0\).

Complex multiplication

The elliptic curves in class 95139a do not have complex multiplication.

Modular form 95139.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 4 q^{5} - 2 q^{7} - 3 q^{8} + 4 q^{10} - q^{11} + 2 q^{13} - 2 q^{14} - q^{16} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.