Properties

Label 14586.k
Number of curves $2$
Conductor $14586$
CM no
Rank $1$
Graph

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

Elliptic curves in class 14586.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.k1 14586j1 \([1, 1, 1, -84338, -9461761]\) \(66342819962001390625/4812668669952\) \(4812668669952\) \([2]\) \(59136\) \(1.4847\) \(\Gamma_0(N)\)-optimal
14586.k2 14586j2 \([1, 1, 1, -78898, -10728193]\) \(-54315282059491182625/17983956399469632\) \(-17983956399469632\) \([2]\) \(118272\) \(1.8312\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14586.k have rank \(1\).

Complex multiplication

The elliptic curves in class 14586.k do not have complex multiplication.

Modular form 14586.2.a.k

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.