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Properties

Label 14490g
Number of curves $2$
Conductor $14490$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 14490g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.d1 14490g1 \([1, -1, 0, -46485, 3866485]\) \(15238420194810961/12619514880\) \(9199626347520\) \([2]\) \(53760\) \(1.4159\) \(\Gamma_0(N)\)-optimal
14490.d2 14490g2 \([1, -1, 0, -36405, 5582101]\) \(-7319577278195281/14169067365600\) \(-10329250109522400\) \([2]\) \(107520\) \(1.7625\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.g

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