Properties

Label 96b
Number of curves 4
Conductor 96
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("96.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 96b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
96.a3 96b1 [0, -1, 0, -2, 0] [2, 2] 4 \(\Gamma_0(N)\)-optimal
96.a1 96b2 [0, -1, 0, -32, -60] [2] 8  
96.a2 96b3 [0, -1, 0, -17, 33] [4] 8  
96.a4 96b4 [0, -1, 0, 8, -8] [2] 8  

Rank

sage: E.rank()
 

The elliptic curves in class 96b have rank \(0\).

Modular form 96.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + 4q^{7} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.