Properties

Label 494190.v
Number of curves $4$
Conductor $494190$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("494190.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 494190.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
494190.v1 494190v3 [1, -1, 0, -1615275, 789420411] [2] 10485760 \(\Gamma_0(N)\)-optimal*
494190.v2 494190v2 [1, -1, 0, -132705, 3954825] [2, 2] 5242880 \(\Gamma_0(N)\)-optimal*
494190.v3 494190v1 [1, -1, 0, -80685, -8748459] [2] 2621440 \(\Gamma_0(N)\)-optimal*
494190.v4 494190v4 [1, -1, 0, 517545, 30875175] [2] 10485760  
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 494190.v3.

Rank

sage: E.rank()
 

The elliptic curves in class 494190.v have rank \(0\).

Modular form 494190.2.a.v

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

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 LMFDB 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 LMFDB labels.