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Properties

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

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 90354.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90354.n1 90354o2 \([1, 1, 1, -4662158, -3880171573]\) \(-5979677811120816625/6457751764992\) \(-12102866505629171712\) \([]\) \(3556224\) \(2.5775\)  
90354.n2 90354o1 \([1, 1, 1, 6132, 2008509]\) \(13605635375/935384208\) \(-1753060602649488\) \([]\) \(508032\) \(1.6046\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 90354.2.a.n

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.