Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.z1 97020bu4 [0, 0, 0, -21871983, 20758643318] [2] 11943936  
97020.z2 97020bu2 [0, 0, 0, -18855543, 31514220542] [2] 3981312  
97020.z3 97020bu1 [0, 0, 0, -1173648, 496640333] [2] 1990656 \(\Gamma_0(N)\)-optimal
97020.z4 97020bu3 [0, 0, 0, 4541712, 2379994337] [2] 5971968  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.z

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.