Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("95506.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 95506a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95506.e4 95506a1 [1, 1, 0, -8485, 182733] [2] 299520 \(\Gamma_0(N)\)-optimal
95506.e3 95506a2 [1, 1, 0, -120845, 16115381] [2] 599040  
95506.e2 95506a3 [1, 1, 0, -289385, -60030991] [2] 898560  
95506.e1 95506a4 [1, 1, 0, -317475, -47710717] [2] 1797120  

Rank

sage: E.rank()
 

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

Modular form 95506.2.a.e

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

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.