Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.y1 221067bb2 \([1, -1, 0, -168273, 26610700]\) \(408023180713/1421\) \(1835175983949\) \([2]\) \(737280\) \(1.5726\)  
221067.y2 221067bb1 \([1, -1, 0, -10368, 430051]\) \(-95443993/5887\) \(-7602871933503\) \([2]\) \(368640\) \(1.2260\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 221067.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 2q^{5} - q^{7} - 3q^{8} - 2q^{10} + 2q^{13} - q^{14} - q^{16} + 4q^{17} - 2q^{19} + O(q^{20})\)  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.