Properties

Label 14490.bx
Number of curves $2$
Conductor $14490$
CM no
Rank $1$
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Show commands for: SageMath
sage: E = EllipticCurve("bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14490.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.bx1 14490bj1 \([1, -1, 1, -11477, 467101]\) \(8493409990827/185150000\) \(3644307450000\) \([2]\) \(30720\) \(1.1986\) \(\Gamma_0(N)\)-optimal
14490.bx2 14490bj2 \([1, -1, 1, 943, 1415989]\) \(4716275733/44023437500\) \(-866513320312500\) \([2]\) \(61440\) \(1.5452\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 2q^{11} + 2q^{13} + q^{14} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20})\)  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.