Properties

Label 5390.z
Number of curves $2$
Conductor $5390$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5390.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5390.z1 5390bi2 \([1, 1, 1, -21855, 1234477]\) \(23560326604350529/1375000\) \(67375000\) \([]\) \(7776\) \(0.96704\)  
5390.z2 5390bi1 \([1, 1, 1, -295, 1245]\) \(57954303169/17036800\) \(834803200\) \([]\) \(2592\) \(0.41773\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5390.z have rank \(1\).

Complex multiplication

The elliptic curves in class 5390.z do not have complex multiplication.

Modular form 5390.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} - 2 q^{9} + q^{10} + q^{11} - q^{12} + q^{13} - q^{15} + q^{16} - 2 q^{18} - 2 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.