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Properties

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

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

Elliptic curves in class 90354j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90354.g4 90354j1 \([1, 0, 1, -2105551, 431193986]\) \(402355893390625/201513996288\) \(517029782059249569792\) \([2]\) \(4727808\) \(2.6673\) \(\Gamma_0(N)\)-optimal
90354.g3 90354j2 \([1, 0, 1, -18314511, -29866594046]\) \(264788619837198625/3058196150592\) \(7846494627476035384128\) \([2]\) \(9455616\) \(3.0139\)  
90354.g2 90354j3 \([1, 0, 1, -92459551, -342192619678]\) \(34069730739753390625/1354703543952\) \(3475798659083538628368\) \([2]\) \(14183424\) \(3.2166\)  
90354.g1 90354j4 \([1, 0, 1, -1479338691, -21900396723494]\) \(139545621883503188502625/220644468\) \(566113338547355412\) \([2]\) \(28366848\) \(3.5632\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 90354.2.a.j

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.