Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14490.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.q1 14490q1 \([1, -1, 0, -2205, -37499]\) \(1626794704081/83462400\) \(60844089600\) \([2]\) \(24576\) \(0.82718\) \(\Gamma_0(N)\)-optimal
14490.q2 14490q2 \([1, -1, 0, 1395, -150539]\) \(411664745519/13605414480\) \(-9918347155920\) \([2]\) \(49152\) \(1.1738\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.q

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