Properties

Label 20160dd
Number of curves $4$
Conductor $20160$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20160.di1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.di2 20160dd1 [0, 0, 0, -6732, -212336] [2] 18432 \(\Gamma_0(N)\)-optimal
20160.di3 20160dd2 [0, 0, 0, -4812, -335984] [2] 36864  
20160.di1 20160dd3 [0, 0, 0, -26892, 1487376] [2] 55296  
20160.di4 20160dd4 [0, 0, 0, 42228, 7874064] [2] 110592  

Rank

sage: E.rank()
 

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

Modular form 20160.2.a.di

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.