Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.q1 97020ca2 \([0, 0, 0, -4884663, 4155261838]\) \(1711503051568/7425\) \(55917315279302400\) \([2]\) \(1806336\) \(2.4204\)  
97020.q2 97020ca1 \([0, 0, 0, -300468, 67076737]\) \(-6373654528/441045\) \(-207593032974410160\) \([2]\) \(903168\) \(2.0738\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.q

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