Properties

Label 490.h
Number of curves $4$
Conductor $490$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 490.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
490.h1 490h4 \([1, -1, 1, -13117, 581459]\) \(2121328796049/120050\) \(14123762450\) \([2]\) \(768\) \(1.0119\)  
490.h2 490h3 \([1, -1, 1, -4297, -100229]\) \(74565301329/5468750\) \(643392968750\) \([2]\) \(768\) \(1.0119\)  
490.h3 490h2 \([1, -1, 1, -867, 8159]\) \(611960049/122500\) \(14412002500\) \([2, 2]\) \(384\) \(0.66537\)  
490.h4 490h1 \([1, -1, 1, 113, 711]\) \(1367631/2800\) \(-329417200\) \([4]\) \(192\) \(0.31880\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 490.h have rank \(0\).

Complex multiplication

The elliptic curves in class 490.h do not have complex multiplication.

Modular form 490.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} - 3q^{9} + q^{10} + 4q^{11} + 6q^{13} + q^{16} - 2q^{17} - 3q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.