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Properties

Label 14490h
Number of curves $2$
Conductor $14490$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 14490h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.f2 14490h1 \([1, -1, 0, -75195, 3656421]\) \(64500981545311921/29485596672000\) \(21494999973888000\) \([2]\) \(138240\) \(1.8288\) \(\Gamma_0(N)\)-optimal
14490.f1 14490h2 \([1, -1, 0, -605115, -178530075]\) \(33613237452390629041/532385784000000\) \(388109236536000000\) \([2]\) \(276480\) \(2.1754\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.h

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