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

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()

Elliptic curves in class 97020g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.j2 97020g1 [0, 0, 0, 777, 8078] [] 82944 \(\Gamma_0(N)\)-optimal
97020.j1 97020g2 [0, 0, 0, -20223, 1115478] [] 248832  


sage: E.rank()

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

Complex multiplication

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

Modular form 97020.2.a.g

sage: E.q_eigenform(10)
\(q - q^{5} - q^{11} + 4q^{13} - 3q^{17} - 5q^{19} + O(q^{20})\)  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 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.