Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.u1 97020bz1 [0, 0, 0, -273, 1757] [] 31104 \(\Gamma_0(N)\)-optimal
97020.u2 97020bz2 [0, 0, 0, 987, 8813] [] 93312  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.bz

sage: E.q_eigenform(10)
 
\( q - q^{5} + q^{11} - 5q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.