Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("90354.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.p4 90354q1 [1, 1, 1, -31194747, 57821093769] [2] 21012480 \(\Gamma_0(N)\)-optimal
90354.p2 90354q2 [1, 1, 1, -479788667, 4044744417161] [2, 2] 42024960  
90354.p3 90354q3 [1, 1, 1, -460513147, 4384648936841] [2] 84049920  
90354.p1 90354q4 [1, 1, 1, -7676566907, 258876904472969] [2] 84049920  

Rank

sage: E.rank()
 

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

Modular form 90354.2.a.p

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{10} + q^{11} - q^{12} - 6q^{13} - 4q^{14} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.