Properties

Label 493680go
Number of curves 6
Conductor 493680
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("493680.go1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 493680go

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
493680.go4 493680go1 [0, 1, 0, -14152200, 20487232500] [u'2'] 17694720 \(\Gamma_0(N)\)-optimal
493680.go3 493680go2 [0, 1, 0, -14307080, 20015715828] [u'2', u'2'] 35389440  
493680.go5 493680go3 [0, 1, 0, 7414840, 75441366900] [u'2'] 70778880  
493680.go2 493680go4 [0, 1, 0, -38507080, -65584524172] [u'2', u'2'] 70778880  
493680.go6 493680go5 [0, 1, 0, 101368920, -432451296972] [u'2'] 141557760  
493680.go1 493680go6 [0, 1, 0, -565583080, -5176745911372] [u'2'] 141557760  

Rank

sage: E.rank()
 

The elliptic curves in class 493680go have rank \(1\).

Modular form 493680.2.a.go

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{9} - 6q^{13} + q^{15} - q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.