Properties

Label 97020bk
Number of curves $4$
Conductor $97020$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.f4 97020bk1 [0, 0, 0, 96432, -42349867] [2] 829440 \(\Gamma_0(N)\)-optimal
97020.f3 97020bk2 [0, 0, 0, -1391943, -582034642] [2] 1658880  
97020.f2 97020bk3 [0, 0, 0, -6889008, -6965095543] [2] 2488320  
97020.f1 97020bk4 [0, 0, 0, -110248383, -445560267418] [2] 4976640  

Rank

sage: E.rank()
 

The elliptic curves in class 97020bk have rank \(0\).

Complex multiplication

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

Modular form 97020.2.a.bk

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

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.