Properties

Label 95506a
Number of curves $4$
Conductor $95506$
CM no
Rank $1$
Graph

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

Elliptic curves in class 95506a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95506.e4 95506a1 \([1, 1, 0, -8485, 182733]\) \(3048625/1088\) \(24114824908352\) \([2]\) \(299520\) \(1.2688\) \(\Gamma_0(N)\)-optimal
95506.e3 95506a2 \([1, 1, 0, -120845, 16115381]\) \(8805624625/2312\) \(51244002930248\) \([2]\) \(599040\) \(1.6153\)  
95506.e2 95506a3 \([1, 1, 0, -289385, -60030991]\) \(120920208625/19652\) \(435574024907108\) \([2]\) \(898560\) \(1.8181\)  
95506.e1 95506a4 \([1, 1, 0, -317475, -47710717]\) \(159661140625/48275138\) \(1069987592184310802\) \([2]\) \(1797120\) \(2.1646\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95506a have rank \(1\).

Complex multiplication

The elliptic curves in class 95506a do not have complex multiplication.

Modular form 95506.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - q^{8} + q^{9} + 6 q^{11} + 2 q^{12} + 2 q^{13} + 4 q^{14} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.