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Properties

Label 90774.s
Number of curves $3$
Conductor $90774$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 90774.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90774.s1 90774bd2 \([1, -1, 1, -48224, -4116743]\) \(-132651/2\) \(-186992603551206\) \([]\) \(414720\) \(1.5416\)  
90774.s2 90774bd3 \([1, -1, 1, -23009, 1786929]\) \(-1167051/512\) \(-590988969248256\) \([]\) \(414720\) \(1.5416\)  
90774.s3 90774bd1 \([1, -1, 1, 2206, -28551]\) \(9261/8\) \(-1026022516056\) \([]\) \(138240\) \(0.99228\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 90774.s have rank \(1\).

Complex multiplication

The elliptic curves in class 90774.s do not have complex multiplication.

Modular form 90774.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 3 q^{5} + q^{7} + q^{8} - 3 q^{10} - 3 q^{11} + 4 q^{13} + q^{14} + q^{16} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.