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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 14490j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.e2 14490j1 \([1, -1, 0, -2700, -22064]\) \(2986606123201/1421952000\) \(1036603008000\) \([2]\) \(30720\) \(0.99955\) \(\Gamma_0(N)\)-optimal
14490.e1 14490j2 \([1, -1, 0, -35820, -2598800]\) \(6972359126281921/5071500000\) \(3697123500000\) \([2]\) \(61440\) \(1.3461\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 2 q^{11} - 6 q^{13} + q^{14} + q^{16} - 4 q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.