Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.c1 221067c2 [1, -1, 1, -18041, -864894] [2] 442368  
221067.c2 221067c1 [1, -1, 1, -3686, 71052] [2] 221184 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 221067.c have rank \(2\).

Complex multiplication

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

Modular form 221067.2.a.c

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

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.