Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.a1 221067b2 [0, 0, 1, -2341713, -1379423444] [] 10080000  
221067.a2 221067b1 [0, 0, 1, 21417, -41594] [] 2016000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 221067.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{2} + 2q^{4} + 4q^{5} - q^{7} - 8q^{10} - 4q^{13} + 2q^{14} - 4q^{16} - 2q^{17} - 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.