Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.ba1 221067ba2 \([1, -1, 0, -2182923, 1157722330]\) \(669233048723/50759541\) \(87252801680436806799\) \([2]\) \(4866048\) \(2.5713\)  
221067.ba2 221067ba1 \([1, -1, 0, -445968, -93232661]\) \(5706550403/1112643\) \(1912570860720081177\) \([2]\) \(2433024\) \(2.2247\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 221067.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 2q^{5} + q^{7} - 3q^{8} - 2q^{10} + q^{14} - q^{16} + 2q^{17} - 2q^{19} + O(q^{20})\)  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.