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Properties

Label 90354.j
Number of curves $2$
Conductor $90354$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 90354.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90354.j1 90354i2 \([1, 0, 1, -1120311596, 14425617455210]\) \(60607987148648054544625/35377817158176768\) \(90769799775507463947866112\) \([2]\) \(57784320\) \(3.9261\)  
90354.j2 90354i1 \([1, 0, 1, -82938156, 136420743274]\) \(24591016773082896625/11097062309363712\) \(28472025829453003864670208\) \([2]\) \(28892160\) \(3.5795\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 90354.j do not have complex multiplication.

Modular form 90354.2.a.j

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

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.