Properties

Label 97020h
Number of curves $2$
Conductor $97020$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.a1 97020h1 [0, 0, 0, -21168, 1083537] [2] 387072 \(\Gamma_0(N)\)-optimal
97020.a2 97020h2 [0, 0, 0, 25137, 5167638] [2] 774144  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{11} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.