Properties

Label 20160.i
Number of curves $4$
Conductor $20160$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.i1 20160bf3 [0, 0, 0, -215148, -38410832] [2] 98304  
20160.i2 20160bf2 [0, 0, 0, -13548, -590672] [2, 2] 49152  
20160.i3 20160bf1 [0, 0, 0, -2028, 22192] [2] 24576 \(\Gamma_0(N)\)-optimal
20160.i4 20160bf4 [0, 0, 0, 3732, -1993808] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 20160.i have rank \(0\).

Complex multiplication

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

Modular form 20160.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 4q^{11} + 2q^{13} + 6q^{17} + O(q^{20}) \)

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.