Properties

Label 14490.k
Number of curves $2$
Conductor $14490$
CM no
Rank $0$
Graph

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

Elliptic curves in class 14490.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.k1 14490c1 \([1, -1, 0, -44339415, 47524672925]\) \(489781415227546051766883/233890092903563264000\) \(4603658698620835725312000\) \([2]\) \(3096576\) \(3.4263\) \(\Gamma_0(N)\)-optimal
14490.k2 14490c2 \([1, -1, 0, 159149865, 361345840541]\) \(22649115256119592694355357/15973509811739648000000\) \(-314406593624471491584000000\) \([2]\) \(6193152\) \(3.7729\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14490.k have rank \(0\).

Complex multiplication

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

Modular form 14490.2.a.k

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.