Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("490.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 490h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
490.h4 490h1 [1, -1, 1, 113, 711] [4] 192 \(\Gamma_0(N)\)-optimal
490.h3 490h2 [1, -1, 1, -867, 8159] [2, 2] 384  
490.h2 490h3 [1, -1, 1, -4297, -100229] [2] 768  
490.h1 490h4 [1, -1, 1, -13117, 581459] [2] 768  

Rank

sage: E.rank()
 

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

Modular form 490.2.a.h

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.