Properties

Label 14490.ca
Number of curves $2$
Conductor $14490$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14490.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.ca1 14490bi1 \([1, -1, 1, -4926602, -1758530871]\) \(489781415227546051766883/233890092903563264000\) \(6315032508396208128000\) \([2]\) \(1032192\) \(2.8770\) \(\Gamma_0(N)\)-optimal
14490.ca2 14490bi2 \([1, -1, 1, 17683318, -13389073719]\) \(22649115256119592694355357/15973509811739648000000\) \(-431284764916970496000000\) \([2]\) \(2064384\) \(3.2236\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14490.ca have rank \(1\).

Complex multiplication

The elliptic curves in class 14490.ca do not have complex multiplication.

Modular form 14490.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 2q^{11} - 6q^{13} + q^{14} + q^{16} - 6q^{17} + O(q^{20})\)  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.