Properties

Label 97020n
Number of curves $2$
Conductor $97020$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.o1 97020n1 [0, 0, 0, -15156288, 22711055913] [2] 3594240 \(\Gamma_0(N)\)-optimal
97020.o2 97020n2 [0, 0, 0, -15109983, 22856722182] [2] 7188480  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.n

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

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.