Properties

Label 90354d
Number of curves 2
Conductor 90354
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("90354.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.d2 90354d1 [1, 1, 0, 8394680, 101611095184] [] 18797184 \(\Gamma_0(N)\)-optimal
90354.d1 90354d2 [1, 1, 0, -6382494330, -196446593263212] [] 131580288  

Rank

sage: E.rank()
 

The elliptic curves in class 90354d have rank \(0\).

Modular form 90354.2.a.d

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.