Properties

Label 221067.g
Number of curves $2$
Conductor $221067$
CM no
Rank $1$
Graph

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

Elliptic curves in class 221067.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.g1 221067f1 \([1, -1, 1, -320, 938]\) \(3723875/1827\) \(1772736273\) \([2]\) \(79872\) \(0.46791\) \(\Gamma_0(N)\)-optimal
221067.g2 221067f2 \([1, -1, 1, 1165, 6284]\) \(180362125/123627\) \(-119955154473\) \([2]\) \(159744\) \(0.81448\)  

Rank

sage: E.rank()
 

The elliptic curves in class 221067.g have rank \(1\).

Complex multiplication

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

Modular form 221067.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{7} + 3q^{8} + 2q^{13} - q^{14} - q^{16} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.