Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.a1 97020h1 \([0, 0, 0, -21168, 1083537]\) \(28311552/2695\) \(99852348713040\) \([2]\) \(387072\) \(1.4241\) \(\Gamma_0(N)\)-optimal
97020.a2 97020h2 \([0, 0, 0, 25137, 5167638]\) \(2963088/21175\) \(-12552866695353600\) \([2]\) \(774144\) \(1.7707\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.