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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 5390.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5390.k1 5390g2 \([1, -1, 0, -144440, -12055744]\) \(971613907622044623/378125000000000\) \(129696875000000000\) \([2]\) \(64512\) \(1.9825\)  
5390.k2 5390g1 \([1, -1, 0, -126520, -17284800]\) \(652993822364173263/225280000000\) \(77271040000000\) \([2]\) \(32256\) \(1.6359\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5390.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} - 3 q^{9} + q^{10} + q^{11} - 2 q^{13} + q^{16} - 8 q^{17} + 3 q^{18} + 4 q^{19} + O(q^{20})\) 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.