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Properties

Label 221067.q
Number of curves $2$
Conductor $221067$
CM no
Rank $0$
Graph

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

Elliptic curves in class 221067.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.q1 221067q1 [0, 0, 1, -68970, 10505250] [] 1209600 \(\Gamma_0(N)\)-optimal
221067.q2 221067q2 [0, 0, 1, 562650, -162148077] [] 3628800  

Rank

sage: E.rank()
 

The elliptic curves in class 221067.q have rank \(0\).

Complex multiplication

The elliptic curves in class 221067.q do not have complex multiplication.

Modular form 221067.2.a.q

sage: E.q_eigenform(10)
 
\( q - 2q^{4} - q^{7} - 2q^{13} + 4q^{16} + 6q^{17} + 7q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.