Properties

Label 159936.go
Number of curves $4$
Conductor $159936$
CM no
Rank $0$
Graph

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

Elliptic curves in class 159936.go

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159936.go1 159936o3 \([0, 1, 0, -15927809, 24461764095]\) \(14489843500598257/6246072\) \(192634978232696832\) \([2]\) \(7077888\) \(2.6592\)  
159936.go2 159936o4 \([0, 1, 0, -2129409, -632909313]\) \(34623662831857/14438442312\) \(445295702721033142272\) \([2]\) \(7077888\) \(2.6592\)  
159936.go3 159936o2 \([0, 1, 0, -1000449, 377961471]\) \(3590714269297/73410624\) \(2264055546636140544\) \([2, 2]\) \(3538944\) \(2.3127\)  
159936.go4 159936o1 \([0, 1, 0, 3071, 17697791]\) \(103823/4386816\) \(-135293702133252096\) \([2]\) \(1769472\) \(1.9661\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 159936.go have rank \(0\).

Complex multiplication

The elliptic curves in class 159936.go do not have complex multiplication.

Modular form 159936.2.a.go

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{5} + q^{9} - 6q^{13} - 2q^{15} - q^{17} + O(q^{20})\)  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.