Properties

Label 90354.t
Number of curves 2
Conductor 90354
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("90354.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.t1 90354x1 [1, 0, 0, -50578418, 133339353924] [2] 17335296 \(\Gamma_0(N)\)-optimal
90354.t2 90354x2 [1, 0, 0, 24388022, 494812534316] [2] 34670592  

Rank

sage: E.rank()
 

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

Modular form 90354.2.a.t

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.