Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("90354.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.o1 90354n2 [1, 1, 1, -76008, 7265469] [2] 525312  
90354.o2 90354n1 [1, 1, 1, 6132, 562845] [2] 262656 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 90354.2.a.o

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

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 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.