Properties

Label 90354.g
Number of curves 4
Conductor 90354
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("90354.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.g1 90354j4 [1, 0, 1, -1479338691, -21900396723494] [2] 28366848  
90354.g2 90354j3 [1, 0, 1, -92459551, -342192619678] [2] 14183424  
90354.g3 90354j2 [1, 0, 1, -18314511, -29866594046] [2] 9455616  
90354.g4 90354j1 [1, 0, 1, -2105551, 431193986] [2] 4727808 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 90354.g have rank \(1\).

Modular form 90354.2.a.g

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

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.