Properties

Label 97020.d
Number of curves $4$
Conductor $97020$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.d1 97020f3 [0, 0, 0, -2931768, 1932150213] [2] 1492992  
97020.d2 97020f4 [0, 0, 0, -2885463, 1996134462] [2] 2985984  
97020.d3 97020f1 [0, 0, 0, -50568, 353633] [2] 497664 \(\Gamma_0(N)\)-optimal
97020.d4 97020f2 [0, 0, 0, 201537, 2824262] [2] 995328  

Rank

sage: E.rank()
 

The elliptic curves in class 97020.d have rank \(1\).

Complex multiplication

The elliptic curves in class 97020.d do not have complex multiplication.

Modular form 97020.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.