Properties

Label 90.a
Number of curves 4
Conductor 90
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("90.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90.a1 90a4 [1, -1, 0, -1149, -14707] [2] 48  
90.a2 90a3 [1, -1, 0, -69, -235] [2] 24  
90.a3 90a2 [1, -1, 0, -24, 18] [6] 16  
90.a4 90a1 [1, -1, 0, 6, 0] [6] 8 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 90.a have rank \(0\).

Modular form 90.2.a.a

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

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 LMFDB 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 LMFDB labels.