Properties

Label 20160du
Number of curves $3$
Conductor $20160$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("du1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.bb2 20160du1 \([0, 0, 0, -48, 142]\) \(-262144/35\) \(-1632960\) \([]\) \(2880\) \(-0.075270\) \(\Gamma_0(N)\)-optimal
20160.bb3 20160du2 \([0, 0, 0, 312, -362]\) \(71991296/42875\) \(-2000376000\) \([]\) \(8640\) \(0.47404\)  
20160.bb1 20160du3 \([0, 0, 0, -4728, -130898]\) \(-250523582464/13671875\) \(-637875000000\) \([]\) \(25920\) \(1.0233\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20160du have rank \(1\).

Complex multiplication

The elliptic curves in class 20160du do not have complex multiplication.

Modular form 20160.2.a.du

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + 3q^{11} - 5q^{13} - 3q^{17} + 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.